Evaluate the integral.
-$\int _ { 0 } ^ { 1 } 5 x 4 \sqrt { x ^ { 5 } + 4 }$ dx
A) $\frac { 10 \sqrt { 5 } + 16 } { 3 }$
B) $\frac { 10 \sqrt { 5 } - 16 } { 15 }$
C) $\frac { 10 \sqrt { 5 } - 16 } { 3 }$
D) 2 $\sqrt { 5 }$ -4

Question

Evaluate the integral. 
-$\int _ { 0 } ^ { 1 } 5 x 4 \sqrt { x ^ { 5 } + 4 }$ dx
A) $\frac { 10 \sqrt { 5 } + 16 } { 3 }$
B) $\frac { 10 \sqrt { 5 } - 16 } { 15 }$
C) $\frac { 10 \sqrt { 5 } - 16 } { 3 }$
D) 2 $\sqrt { 5 }$ -4

Quizplus · Accepted Answer

The integral can be solved using substitution. Let $ u = x^5 + 4 $, then $ du = 5x^4 dx $. The limits change accordingly, and the integral simplifies to $\int \sqrt{u} \, du$, which evaluates to $\frac{2}{3} u^{3/2}$. Substituting back and evaluating from 0 to 1 gives the result $\frac { 10 \sqrt { 5 } - 16 } { 3 }$.

Evaluate the Integral ∫015x4x5+4\int _ { 0 } ^ { 1 } 5 x 4 \sqrt { x ^ { 5 } + 4 }∫01​5x4x5+4​

Evaluate the Integral $\int _ { 0 } ^ { 1 } 5 x 4 \sqrt { x ^ { 5 } + 4 }$