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Question

Question: <img src="https://cdn.pureessence.tech/canvas_421.png?top_left_x=1500&top_left_y=1260&width=300&heig...

is equal to

A

7/3

B

14/3

C

28/3

D

1/3

Answer

28/3

Explanation

Solution

I =+ ∫13(−1+x2)dx\int _ { 1 } ^ { 3 } \left( - 1 + x ^ { 2 } \right) d x

= [−x+x33]−2−1\left[ - x + \frac { x ^ { 3 } } { 3 } \right] _ { - 2 } ^ { - 1 } + [x−x33]−11\left[ x - \frac { x ^ { 3 } } { 3 } \right] _ { - 1 } ^ { 1 } +

= (23+23)\left( \frac { 2 } { 3 } + \frac { 2 } { 3 } \right) + (23+23)\left( \frac { 2 } { 3 } + \frac { 2 } { 3 } \right) + (6+23)\left( 6 + \frac { 2 } { 3 } \right) = 28/3