advertisement

MATH 101 HOMEWORK 3 Due on Wednesday Sept. 24 Covers sections 5.4–5.6. For full credit, please show all work. 1. (2 marks) We know that the average value of f (x) = x3 + 1 on some interval [a, b] is 9. Prove that b ≥ 2. Can we say anything about a? 0 Z sin x 2 ex 2. (3 marks) Find F (x), if F (x) = +t2 dt. 0 3. (9 marks) Evaluate the integrals: Z 3π/2 (a) | sin5 x| dx, 0 Z (b) Z (c) 1 2 x2 − x + 1 √ dx, x dx . ex + e−x 4. (6 marks) Evaluate the areas of the following planar regions: (a) the region bounded from below by the lines y = x and y = −x, and from above by the parabola y = 2 − x2 , (b) the region bounded by the half-parabola y = x2 , x ≥ 0; the half-parabola y = (x − 2)2 , x ≥ 2; and the horizontal lines y = a2 and y = b2 . 1