lab9_f11 - Math 116 Lab 9 Fall 2011 Integration by...

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Math 116 - Lab 9 - Fall 2011. Integration by Substitution, Average Value of a Function, Curve Length (Sections 6.1, 7.7 and 7.1 of L/G). You are to provide full solutions to the following problems. You are allowed to collaborate with your classmates, use your notes and textbook and ask the TA for guidance. Direct copying of solutions is not encouraged, nor is it allowed or ethical. Last name: First name: Student number: 1
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Math 116 - Lab 9 - Fall 2011. Student number: 1. Compute the following integrals by substitution. a) integraltext sin(3 x ) dx b) integraltext exp( t + 3) dt c) integraltext (3 t 3 + 7) 4 t 2 dt d) integraldisplay t 3 t 2 + 5 dt e) integraldisplay 3 x 2 1 + x 6 dx (Hint: recall the derivative of arctan( x ).) f) integraldisplay 1 t 2 + 2 t + 5 dt (Hint: recall the derivative of arctan( x ) and complete the square.) g) integraldisplay t exp( t 2 + 1) 1 + exp(2 t 2 + 2) dt (Hint: recall the derivative of arctan( x ).) h) integraldisplay tan( t ) cos( t ) dt i) integraldisplay cos( t ) sin( t ) dt j) integraldisplay t cos 2 ( t 2 + 1) dt k) integraltext sin 2 ( t ) cos( t ) dt l) integraltext sin 5 ( t ) cos 10 ( t ) dt m) integraldisplay
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