# HW3 (1).pdf - Homework 3 Due October 18, 2019 1. Calculate...

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Homework 3Due October 18, 20191. Calculate the following integrals:(a)Z011-x dx(b)Zπ0cosx2dx(c)Z2-2|x|dx2. Calculate the derivative ofZx20cost dtin two ways: by using FTC I, and by doing the integration and differ-entiating directly.3. Given functionsg(x) andh(x), calculateZ10g(x)h00(x)-h(x)g00(x)dx. (Hint: try to see what other pieces youmight need if each piece of the integrand arose from a (separate) product rule.)4. Find the area between the following functions, in the region bounded by them:(a)xandx2(b) sinxand2xπ(Here, there are two regions, one above and one below thex-axis. I want the total area ofboth, counting each as positive area.)(c) 2x,x/2, and 6-x(Hint: the best way to solve these is to draw them on a graph and try to find their intersection points.)5. Find the constantcso that the vertical linex=cdivides the area betweeny=x+ 1, they-axis, thex-axisand the linex= 6 into equal parts.6. Calculate the following functions:(a)Z4-x dx(b)Z2xe-x2dx(c)f(x) so thatf00(x) =2x3,f

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Term
Fall
Professor
townsend
Tags
Cubic function, Quintic equation, functions g
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