MATH 151 TEST 1 SPRING 2010 3 4 2010 Remember to keep your work neat and orderly Show all of your work NO WORK NO CREDIT Read each question carefully and be sure to answer the question that was asked Good luck Name pts 1 Find the partial fractions expansion for each of the following Find the coefficients 3 x 10 a x 2 x 2 b 6 4x2 x 3 x 1 x 2 5 2 Set up an integral or integrals to find the area of the triangle bounded by the lines y 6 x 1 2 and y x 6 y 2x 5 3 Set up integral s do not integrate that will give the volume if the region bounded by the curves y 8 and y x 2 4 x 8 is revolved around a The x axis b The y axis 4 Integrate each of the following 5 5 7x 3 dx a 4 x2 2 3 b 3 x cos 5 x dx 4 c x x 5 x 5 2 dx d 5 16 9 x 2 dx 9 8 7 7 5 Set up two different formulas using an integral s one with a dx and one with a dy that will give the volume if the region bounded by the y axis and the lines y 3 x and y 2 x is revolved around the y axis Do not integrate a Use dx b Use dy 5 6 6 Evaluate the following integral by doing a u substitution and changing the limits to u limits 2 x x 2 5 2 dx 0 6 7 State how you would integrate each of the following If you state u substitution u sub what is u and du If you state partial fractions PF what is the form of the expansion If you state integration by parts IBP how many times do you need to do it and what is the first u and dv 3x 5 2 dx a 2 x 2x 8 b 3x c 5 ln x dx d 5 x cos x 3 3 sin 2 x dx 2 3 3 dx 8 Give the form of the partial fractions expansion do not solve of x3 2x 8 x x 5 3 x 2 6 2 5 dy dy dt 9 Using the parametric equations x t 4t 1 y t 2 dx dx dt a Find the equation and then sketch the curve in the x y plane Show the initial point t 0 and the direction of motion 2 b Find the slope of the tangent line to the curve in the x y plane at t 1 5 3