Evaluate the integral. $\int _ { 7 } ^ { 15 } \left( x ^ { 3 } - 43 x \right) \mathrm { d } x$
A)8,272
B) 88
C) 12,056
D) 20,328
E) 3,792

Question

Evaluate the integral.   $\int _ { 7 } ^ { 15 } \left( x ^ { 3 } - 43 x \right) \mathrm { d } x$  
A)8,272
B) 88
C) 12,056
D) 20,328
E) 3,792

Quizplus · Accepted Answer

The integral of $x^3 - 43x$ from 7 to 15 can be calculated by finding the antiderivative, which is $\frac{1}{4}x^4 - \frac{43}{2}x^2$, and then evaluating it from 7 to 15. This gives:$$\left[\frac{1}{4}(15)^4 - \frac{43}{2}(15)^2\right] - \left[\frac{1}{4}(7)^4 - \frac{43}{2}(7)^2\right] = 8,272.$$

Evaluate the Integral ∫715(x3−43x)dx\int _ { 7 } ^ { 15 } \left( x ^ { 3 } - 43 x \right) \mathrm { d } x∫715​(x3−43x)dx

Evaluate the Integral $\int _ { 7 } ^ { 15 } \left( x ^ { 3 } - 43 x \right) \mathrm { d } x$