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Unformatted text preview: u = t and dv = e-t dt . Then du = dt and v =-e-t . Thus, Z 2 te-t dt = h-e-t t i 2-Z 2-e-t dt = h-e-t t i 2-h e-t i 2 =-e-2 2 + e-2-1 . 1 Question 3: Sketch 2 x 2 and sin x from-1 to 1. Hence nd R 1-1 (2 x 2 +sin x ) dx using symmetry. Check your answer by an explicit calculation. Answer: You will have to provide the sketch yourselves, because I have not yet worked out how to do that in Latex. From your diagram you will hopefully be able to tell that the integral of sin x is going to cancel out, since sin is odd. So R 1-1 (2 x 2 + sin x ) dx = R 1-1 2 x 2 dx = 4 R 1 x 2 = 4 3 2...
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