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Question: To find the numerical value of \(\int _ { - 2 } ^ { 2 } \left( p x ^ { 2 } + q x + s \right) d x\) ...

To find the numerical value of ∫−22(px2+qx+s)dx\int _ { - 2 } ^ { 2 } \left( p x ^ { 2 } + q x + s \right) d x it is necessary to know the values of constants

A

B

qq

C

D

and

Answer

and

Explanation

Solution

Given integral

I=∫−22(px2+s)dx+q∫−22xdxI = \int _ { - 2 } ^ { 2 } \left( p x ^ { 2 } + s \right) d x + q \int _ { - 2 } ^ { 2 } x d x

I=2∫02(px2+s)dx+0=43(4p+3s)I = 2 \int _ { 0 } ^ { 2 } \left( p x ^ { 2 } + s \right) d x + 0 = \frac { 4 } { 3 } ( 4 p + 3 s )

Thus, to find the numerical value of I, it is necessary to know the value of p and s.