MA 23200NAME: Exam 1PUID:INSTRUCTIONS• No books or notes are allowed.• You may use a one-line scientific calculator. No other electronic device is allowed.Be sure to turn off your cellphone.• Show all your work in the space provided. Little or no credit may be given foran answer with insufficient or inconsistent work, even if the answer happens to becorrect.• Write answers in the boxes provided. All answers are expected to be simplified(24→12, 2x + x → 3x, eln 2→ 2, etc).Question Possible Score1 82 83 104 105 106 87 88 109 1010 1011 8Total 100The Trapezoid Rule for estimating the integralRbaf(x)dx with n trapezoids is given byTn=12∆x [f(x0) + 2f(x1) + ··· + 2f(xn−1) + f(xn)]where ∆x =b−an, x0= a, x1= a + ∆x, x2= a + 2∆x, . . . , xn= a + n∆x = b.1For Problems 1 - 5, evaluate the given integrals. On the problems 1 through 3,use the substitution method. On problems 4 and 5, use integration by parts.1.) (8 pts)Ze3x1 + 2e3xdx2.) (8 pts)Z10(5x − 2)4dx23.) (10 pts)Z21x2(1 + x3)2dx4.) (10 pts)Z51ln tt2dt35.) (10 pts)Zx2cos 3xdx.6.) (8 pts) Find the area under the graph of the function f(x) over the interval [−1, 4]wheref(x) =2 − x, if x < 1x2, if x ≥ 1.47.) (8 pts) Approximate the integralZ1−111 + x2dxusing the Trap ezoid Rule with n = 4. (See page 1.)T4=8.) (10 pts) Determine whether the integralZ∞0xe−4xdxis convergent or divergent. If it converges, calculate its value.59.) (10 pts) Find the volume generated by revolving about the x-axis the region undery =1x+ x from x = 1 to x = 5.V=10.) (10 pts) Find the volume of the solid that, for 0 ≤ x ≤ 2, has cross-sections that aretriangles with base 2x2and height 3x + 1.V =611.) (8 pts) Evaluate the following integral by substitution:Zx√x + 1dxHint: Use integration by