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CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS
Chapter 8. APPLICATION OF INTEGRALS
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1 10420
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration calculate the area of the region bounded by
the two parabolas and Click to watch Free Video Solution of this question on Doubtnut
2 10493
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area of the region bounded by the parabola
and the line Click to watch Free Video Solution of this question on Doubtnut
3 10512
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area of the region enclosed between
the circles Click to watch Free Video Solution of this question on Doubtnut
y = x2 x = y2
x2 = 4y\ x = 4y − 2
x2 + y2 = 1 and (x − 1)2 + y2 = 1
4 10558
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area of that part of the circle which is
exterior to the parabola Click to watch Free Video Solution of this question on Doubtnut
5 10573
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration find the area of the region bounded by the
parabola and the circle Click to watch Free Video Solution of this question on Doubtnut
6 10619
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using the method of integration, find the area of the region
bounded by the lines and
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7 10625 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
x2 + \ y2 = 16
y2 = 6x.
y2 = 4x 4x2 + 4y2 = 9
2x + y = 4, 3x − 2y = 6
3y + 5 = 0
Using the method of integration, find the area of the region
bounded by the lines :
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8 10641
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using the method of integration, find the area of the region
bounded by the lines
Click to watch Free Video Solution of this question on Doubtnut
9 10667
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Sketch the graph of and evaluate the area under
the curve above xaxis and between to
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10 10679 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
2x + y = 4 3x − 2y = 6
x − 3y + 5 = 0
3x − 2y + 1 = 0, 2x + 3y − 21 = 0 and x − 5y + 9
= 0.
y = |x + 3|
y = |x + 3| x = 6
x = 0.
Find the area enclosed by the parabola and the line
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11 10683
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area bounded by the curve
and the line Click to watch Free Video Solution of this question on Doubtnut
12 10697
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area of the triangle ABC,
coordinates of whose vertices are A(4,1), B(6,6) and C(8,4) Click to watch Free Video Solution of this question on Doubtnut
13 10698 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area of circle which is interior to the
parabola
4y = 3x2
2y = 3x + 12.
x2 = 4y
x = 4y − 2.
4x2 + 4y2 = 9
x2 = 4y
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14 10757
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area of the region in the first quadrant enclosed by
the line and the circle Click to watch Free Video Solution of this question on Doubtnut
15 10795
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the equation of the tangent to the curve
which is parallel to the line Click to watch Free Video Solution of this question on Doubtnut
16 10829
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area of the region
Click to watch Free Video Solution of this question on Doubtnut
17 10940 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
x − aξs, x = √3 y x2 + y2 = 4.
y = √3x − 2
4x − 2y + 5 = 0.
{(x, y) :x2 + y2 ≤ 4, x + y ≥ 2}
Find the area of the region bounded by the parabola
and . Click to watch Free Video Solution of this question on Doubtnut
18 10959
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area of the region enclosed between
the two circles and Click to watch Free Video Solution of this question on Doubtnut
19 10965
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area of the region included between the parabola
and the line . Click to watch Free Video Solution of this question on Doubtnut
20 10972 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
y = x2
y = |x|
x2 + y2 = 4 (x − 2)2 + y2 = 4.
y2 = x x + y = 2
Find the equation of line through the intersection of lines
3x+4y=7 and xy+2=0 and whose slope is 5. Click to watch Free Video Solution of this question on Doubtnut
21 11051
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area of the following region :
Click to watch Free Video Solution of this question on Doubtnut
22 11052
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area of the region bounded by the
lines, and
Click to watch Free Video Solution of this question on Doubtnut
23 13358
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the areas of the region
using integration. Click to watch Free Video Solution of this question on Doubtnut
{(x, y); |x + 2| ≤ y ≤ √20 − x2}
4x − y + 5 = 0; x + y − 5 = 0
x − 4y + 5 = 0
{x, y}: y2 ≤ 4x, 4x2 + 4y2 ≤ 9},
24 13359
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area enclosed by the parabola
and the line . Click to watch Free Video Solution of this question on Doubtnut
25 13388
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area of the region in the first quadrant enclosed by the
yaxis, the line and the circle using
integration. Click to watch Free Video Solution of this question on Doubtnut
26 13409
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area of the region bounded by the
line , the curve and Click to watch Free Video Solution of this question on Doubtnut
27 13442 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
4y = 3x2 2y = 3x + 12
y = x x2 + y2 = 32,
xy + 2 = 0 x = √y y − aξs.
Prove that the curves and divide the area
of square bounded by and into
three equal parts. Click to watch Free Video Solution of this question on Doubtnut
28 13459
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration find the area of the region
Click to watch Free Video Solution of this question on Doubtnut
29 13504
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration find the area of the region bounded by the
curves and the xaxis. Click to watch Free Video Solution of this question on Doubtnut
30 228056 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
y2 = 4x x2 = 4y
x = 0, x = 4, y = 4 y = 0
{x, y) :x2 + y2 ≤ 2ax, y2 ≥ ax, x, y ≥ 0}.
y = √4 − x2, x2 + y2 − 4x = 0
Using integration, find the area of region bounded by the
triangle whose vertices are . Click to watch Free Video Solution of this question on Doubtnut
31 228169
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using integration, find the area of the triangle ABC,
coordinates of whose vertices are A(4,1), B(6,6) and C(8,4) Click to watch Free Video Solution of this question on Doubtnut
32 228213
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Using the method of integration, find the area of the triangle
ABC, coordinates of whose vertices are A (1, 2), B (2, 0) and C
(4, 3). Click to watch Free Video Solution of this question on Doubtnut
33 228342 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
(– 2, 1), (0, 4) and (2, 3)
Find the area enclosed between the parabola and
the straight line Click to watch Free Video Solution of this question on Doubtnut
34 228352
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area bounded by the circle x 2 + y2 = 16 and the line
3y = x in the first quadrant, using integration. Click to watch Free Video Solution of this question on Doubtnut
35 228354
CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
Find the area bounded by the circle and the
line in the first quadrant, using integration. Click to watch Free Video Solution of this question on Doubtnut
36 1166939 CLASS 12 BOARDS: MOST IMPORTANT QUESTIONS Chapter 8. APPLICATION OF INTEGRALS
4y = 3x2
3x − 2y + 12 = 0
x2 + y2 = 16
√3y = x
Find the area of the region in the first quadrant enclosed by the
xaxis, the line , and the circle . Click to watch Free Video Solution of this question on Doubtnut
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y = x x2 + y2 = 32