Evaluate the integral by using a substitution prior to integration by parts.
-$$\int _ { 0 } ^ { 1 } \frac { x } { \sqrt { x + 1 } } d x$$
A) $- 1.33$
B) $- 2.27$
C) $- 0.94$
D) $0.39$

Question

Quizplus · Accepted Answer

The integral can be solved by first making a substitution, such as $u = x + 1$, which simplifies the integral and then applying integration by parts if necessary. However, in this case, after the substitution, the integral becomes straightforward and can be directly integrated without needing integration by parts. The correct answer is obtained by evaluating the integral after substitution, which yields a positive value, indicating that option D is correct.

Evaluate the Integral by Using a Substitution Prior to Integration ∫01xx+1dx\int _ { 0 } ^ { 1 } \frac { x } { \sqrt { x + 1 } } d x∫01​x+1​x​dx

Evaluate the Integral by Using a Substitution Prior to Integration $\int _ { 0 } ^ { 1 } \frac { x } { \sqrt { x + 1 } } d x$