Evaluate the integral. $\int _ { 4 } ^ { 9 } 3 \sqrt { x } \mathrm {~d} x$
A)38
B) 85.5
C) 10
D) 19
E) 2

Question

Evaluate the integral.  $\int _ { 4 } ^ { 9 } 3 \sqrt { x } \mathrm {~d} x$  
A)38
B) 85.5
C) 10
D) 19
E) 2

Quizplus · Accepted Answer

The integral $\int _ { 4 } ^ { 9 } 3 \sqrt { x } \mathrm {~d} x$ can be solved by first recognizing that $3\sqrt{x} = 3x^{1/2}$. The antiderivative of $x^{n}$ is $\frac{x^{n+1}}{n+1}$, so the antiderivative of $3x^{1/2}$ is $3 \cdot \frac{x^{3/2}}{3/2} = 2x^{3/2}$. Applying the limits of integration, we get $2(9^{3/2}) - 2(4^{3/2}) = 2(27) - 2(8) = 54 - 16 = 38$.

Evaluate the Integral ∫493x dx\int _ { 4 } ^ { 9 } 3 \sqrt { x } \mathrm {~d} x∫49​3x​ dx

Evaluate the Integral $\int _ { 4 } ^ { 9 } 3 \sqrt { x } \mathrm {~d} x$