Question
Mathematics Question on applications of integrals
The area of the region given by \left\\{(x, y): x y \leq 8,1 \leq y \leq x^2\right\\} is :
A
16loge2−314
B
8loge2−313
C
8loge2+67
D
16loge2+37
Answer
16loge2−314
Explanation
Solution
Area =1∫2(x2−1)dx+2∫8(x8−1)dx
=(3x3)12+8(ℓnx)28−(x)18
=37+8(2ℓn2)−7
=16ln2−314
So, the correct option is (A): 16log e 2−314