10 Questions in Exam 2 - Calculus I | MATH 122, Exams of Calculus

Download 10 Questions in Exam 2 - Calculus I | MATH 122 and more Exams Calculus in PDF only on Docsity! CALCULUS II, MATH 122 EXAM 2 1. Find the exact arc length of the curve over the interval y = 3x3/2 – 1 ; from x = 0 to x = 1 2. Evaluate the given integrals using Integration by Parts (a ) ∫ x ln ( x ) dx (b ) ∫ xTan−1( x ) dx 3. Find the volume of the solid generated when the region enclosed by y = ln(x), the line x=e, and the x-axis is revolved about the x-axis. 4. Use suitable reduction formula to evaluate ∫sin4 (x ) dx 5. Evaluate the given trigonometric integrals (a ) ∫sin2 ( t )cos3( t ) dt (b ) ∫ cot(3 x ) dx 6. Use a suitable method to evaluate the integral ∫sec5 x ) tan3 ( x ) dx [hint: split off a factor of sec(x)tan(x)] 7. Use trigonometric substitution to evaluate the definite integral ∫ 0 1 5 x3√1−x2 dx 8. Find the arc length of the curve y = x2 from x = 0 to x = 1. 9. Write out the form of the partial fraction expansion, do not find numerical values of the coefficients (a ) 2 x−3 x3−x2 (b ) 5 x ( x2−4 ) (c ) 1−3 x4 ( x−2 )( x2+1)2 10. Evaluate the integral ∫ 2x2+3 x (x−1)2 dx ______________________________________________________________________________ ∫sinn( x )dx=− 1 n sinn−1 (x )cos ( x )+ n−1 n ∫ sinn−2 ( x )dx ;∫cosn (x )dx= 1 n cosn−1( x )sin( x )+ n−1 n ∫ cosn−2( x )dx