MATH 152 Midterm: MATH 152 TAMU 2010a Exam 2a Solutions
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To nd the length of the curve y = 4x3/2, 0 x 1, we will use the formula. L = z b a s1 +(cid:18) dy dx(cid:19)2 dy dx. = 6x1/2. dx where a = 0, b = 1 and. Using a u substitution with u = 1 + 36x, we obtain. 1: d. to nd the surface area obtained by rotating the curve y = ex + x, 0 x 1, about the y axis, we will use the formula. 2 xs1 +(cid:18) dy dx(cid:19)2 dx, where a = 0, b = 1 a. = z 1: e: to nd z. 0 x2 x + 3 dx, we must rst perform long division since the power in the denominator is not higher than the power in the numerator. x 3 x + 3) x2. = x 3 + dx = z (cid:18)x 3 + x + 3 x2. 2 3x + 9 ln|x + 3| + c.
