Evaluate the integral. $\int _ { 3 } ^ { 4 } \left( 24 x ^ { 2 } - 1 \right) d x$
given,
$\int _ { 3 } ^ { 4 } x ^ { 3 } d x = \frac { 175 } { 4 }$
$\int _ { 3 } ^ { 4 } x ^ { 2 } d x = \frac { 37 } { 3 }$
$\int _ { 3 } ^ { 4 } x d x = \frac { 7 } { 2 }$
4 $\int _ { 3 } ^ { 4 } d x = 1$
A) 84
B) 1074
C) 8
D) 1346
E) 295

Question

Quizplus · Accepted Answer

The integral $\int _ { 3 } ^ { 4 } \left( 24 x ^ { 2 } - 1 \right) d x$ can be solved by using the given integrals. First, distribute the 24 into the integral of $x^2$, then subtract the integral of 1. Using the given values, $24 \times \frac { 37 } { 3 }$ - 1 = 296 - 1 = 295.

Evaluate the Integral ∫34(24x2−1)dx\int _ { 3 } ^ { 4 } \left( 24 x ^ { 2 } - 1 \right) d x∫34​(24x2−1)dx

Evaluate the Integral $\int _ { 3 } ^ { 4 } \left( 24 x ^ { 2 } - 1 \right) d x$