Test 1 Math 266. ( NO calculator, 11 pt. each)

Find the area enclosed by y = 5x – x2 and y = x. Solve and Draw.

Sketch the region enclosed by x = 2y2 and y = x – 1, set up the integral for the area. Do not solve.

Set up the integrals for the volumes of solids of revolutionRevolve the following triangular templates about the following axes: x = 10, –10, y = 10, –10, find the R and r.

Set up the integral for the following volume shown in shaded region in the picture.

Set up the integral for the following volumea. The solid is a pyramid 60 feet high. The horizontal cross-section x feet from its top is a square of side 3x feet.

b. The solid is a pyramid 40 meters high. The horizontal cross-section x feet from its top is an equilateral triangle of side 6x meters.

c. The base of a solid is a circle of radius 6 cm. All the cross-sections perpendicular to a fixed diameter are equilateral triangles.

Integrations problems from test 1.

∫ tan (x )dx ∫cot (z)dz ∫ sec(θ)dθ ∫ csc( y)dy

∫cosn(x )dx ∫ tann(x )dx ∫ secn(x)dx