# Solutions to Integral and Derivative calculus practice exam, volume of rotation.

May 15th, 2015
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Complete handwritten solutions to all the following questions: 1) Find the equations of the tangent and the normal to the curve y = 1 - sin^2(3x) at the point where x = pi/12. Leave pi in your answer. 2) Find the following: a) integral( 2cot(x)/(sin(2x))dx) b) integral( sin^2(2x)dx) over the integrand x = 0 to x = pi/12 3) Differentiate the following with respect to x: y= ln(sin^2(3x))/(2-3x) 4+5) Find the following indefinite integrals, using the suggested substitution. (problem 4 is same as problem 5) a) integral( 2x^2(1-x^3)^(1/2)dx) , u = 1-x^3 b) integral( e^tan(x)/cos^2(x)dx) over the integrand x = pi/6 to x= pi/4 6) Evaluate the following definite integral using integration by parts. integral( x*cos(2x)dx) over the integrand x = 0 to x = pi/3 7) Find the volume generated when the area enclosed by the curve y=cos(x) is rotated about the x-axis for x = 0 to x = pi/4.

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Name: Solutions to Integral and Derivative calculus practice exam, volume of rotation.Description:Complete handwritten solutions to all the following questions:1) Find the equations of the tangent and the normal to the curve y = 1 - sin^2(3x) at the point where x = pi/12. Leave pi in your answer.2) Find the following: a) integral( 2cot(x)/(sin(2x))dx)b) integral( sin^2(2x)dx) over the integrand x = 0 to x = pi/123) Differentiate the following with respect to x:y= ln(sin^2(3x))/(2-3x)4+5) Find the following indefinite integrals, using the suggested substitution. (problem 4 is same as problem 5)a) integral( 2x^2(1-x^3)^(1/2)dx) , u = 1-x^3b) integral( e^tan(x)/cos^2(x)dx) over the integrand x = pi/6 to x= pi/46) Evaluate the following definite integral using integration by parts.integral( x*cos(2x)dx) over the integrand x = 0 to x = pi/37) Find the volume generated when the area enclosed by the curve y=cos(x) is rotated about the x-axis for x = 0 to x = pi/4.

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