El Use Python to solve each problem. 1. Given the region R bounded by y = (cos x)?, y = 0, r = 0, and a (a) Graph the region R and find its area. (b) Find the volume of the solid formed by rotating R about the e- axis. (c) Find the volume of the solid formed by rotating R about the line 2 = 2 (NOTE: for all three parts, print the integrand, the indefinite integral, and the definite integral-exact and approximate where applicable) 7T C 2. Given g(x) V4 - 12 (a) Model u-substitution by substituting r = 14 W (NOTE this is equivalent to w = 4 x2) into 9(2) (NOTE the denominator -2c is w'), then integrate the resulting expression with respect to w, then re-substitute w = 4-2. (b) Model Integration by Parts by letting u = 22 and dv = V4-22 Find du and v and then print the result from the IBP formula (uv S v du). (c) Model trig substitution by substituting x = 2 sin() into the ex- pression, multiply by da, integrate the resulting expression* with respect to 0, then resubstitute 0 = arcsin *-NOTE: Python does not assume the square root to be positive, so print the resulting expression first and simplify by hand before integrating (d) Your answers should not look the same. Simplify each of them to show that they are algebraically equivalent. El Use Python to solve each problem. 1. Given the region R bounded by y = (cos x)?, y = 0, r = 0, and a (a) Graph the region R and find its area. (b) Find the volume of the solid formed by rotating R about the e- axis. (c) Find the volume of the solid formed by rotating R about the line 2 = 2 (NOTE: for all three parts, print the integrand, the indefinite integral, and the definite integral-exact and approximate where applicable) 7T C 2. Given g(x) V4 - 12 (a) Model u-substitution by substituting r = 14 W (NOTE this is equivalent to w = 4 x2) into 9(2) (NOTE the denominator -2c is w'), then integrate the resulting expression with respect to w, then re-substitute w = 4-2. (b) Model Integration by Parts by letting u = 22 and dv = V4-22 Find du and v and then print the result from the IBP formula (uv S v du). (c) Model trig substitution by substituting x = 2 sin() into the ex- pression, multiply by da, integrate the resulting expression* with respect to 0, then resubstitute 0 = arcsin *-NOTE: Python does not assume the square root to be positive, so print the resulting expression first and simplify by hand before integrating (d) Your answers should not look the same. Simplify each of them to show that they are algebraically equivalent
