Question

A.)Evaluate the following indefinite integral. Do not include +C in your answer. ∫(−2x5+2x−1+3ex)dx

B)Evaluate the following indefinite integral. Do not include +C in your answer.

∫(−6x6−2x3−4)dx

C.)Consider the function f(x)=−2x2+5x+5. If a right Riemann sum with n=4 subintervals is used over the interval [2,4], will the result be an overestimate or an underestimate?

D)Given the function f(x)=2x−4, find the net signed area between f(x) and the x-axis over the interval [−2,9]. Do not include any units in your answer.

Answer 1

A) The indefinite integral of the function is:

-2/6 x^6 + 2/2 x^2 -1x + 3ex

B) The indefinite integral of the function is:

-6/7 x^7 - 2/4 x^4 - 4x

C) A right Riemann sum with n=4 subintervals over the interval [2,4] will be an overestimate of the area under the curve because the function is decreasing on the interval [2,4].

D) The net signed area between f(x) and the x-axis over the interval [-2,9] is:

[2(9)^2 - 4(9)] - [2(-2)^2 - 4(-2)] = 178