Evaluate the definite integral.
-$\int_{0}^{4} \frac{\mathrm{e}^{\mathrm{t}}}{\left(10+\mathrm{e}^{\mathrm{t}}\right)^{3}} d t$
A) 0.0160
B) -0.0024
C) -0.0080
D) 0.0040

Question

Quizplus · Accepted Answer

To solve the integral, use the substitution $ u = 10 + e^t $, which simplifies the integral to $\int \frac{1}{u^3} du$. Evaluating this from the limits $ u(0) = 11 $ to $ u(4) = 10 + e^4 $ gives the result 0.0040.

Evaluate the Definite Integral ∫04et(10+et)3dt\int_{0}^{4} \frac{\mathrm{e}^{\mathrm{t}}}{\left(10+\mathrm{e}^{\mathrm{t}}\right)^{3}} d t∫04​(10+et)3et​dt A) 00160 B) -0

Evaluate the Definite Integral $\int_{0}^{4} \frac{\mathrm{e}^{\mathrm{t}}}{\left(10+\mathrm{e}^{\mathrm{t}}\right)^{3}} d t$ A) 00160
B) -0