M21Ex2F98 - I , T 4 , obtained by partitioning the interval...

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Math 21 Exam 2 1. (10 points) Evaluate Z sin 3 ( x )cos 2 ( x ) dx . 2. (16 points) Determine whether the following integrals converge or diverge; evaluate the integral if it converges; otherwise put DNE . Remember to justify your answer. Calculator work alone is not sufficient for full credit. a) Z 2 0 1 ( x - 1) 2 dx b) Z 3 1 ( x - 2) 3 dx 3. (24 points) Evaluate the following integrals: a) Z 2 x 2 - 2 x dx b) Z 1 0 x +2 x 2 +1 dx (Calculator work alone is not sufficient.) 4. (12 points) Evaluate Z e 1 x 2 ln( x ) dx . (Calculator work alone is not sufficient.) 5. In this problem let I = Z 3 1 cos(3 x ) dx . a) (9 points) Write out, but do not evaluate, the terms in the Trapezoidal Approximation for
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Unformatted text preview: I , T 4 , obtained by partitioning the interval [1 , 3] into 4 subintervals of equal length. b) (5 points) T n is the Trapezoidal Approximation for I , obtained by partitioning the interval [1 , 3] into n subintervals of equal length. How large should n be so that the approximation T n of I is accurate to within . 0001? 6. (24 points) Evaluate the following integrals: a) Z 1 4-x 2 dx b) Z 1 4 x 2 + 16 dx 1...
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