Evaluate the definite integral $\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { 2 x } d x$ . Round your answer to three decimal places.
A)4.195
B)9.486
C)1.597
D)8.986
E)0.473

Question

Quizplus · Accepted Answer

To solve the integral $\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { 2 x } d x$, we can use integration by parts or a tabular method, which is a systematic form of integration by parts. The integral of $x^2e^{2x}$ involves integrating by parts twice, given that we set one part to be differentiated ($x^2$) and the other to be integrated ($e^{2x}$). After applying integration by parts twice, and evaluating the resulting expression from 0 to 1, the correct answer is approximately 1.597.

Evaluate the Definite Integral ∫01x2e2xdx\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { 2 x } d x∫01​x2e2xdx

Evaluate the Definite Integral $\int _ { 0 } ^ { 1 } x ^ { 2 } e ^ { 2 x } d x$