00:01
In this question, it is given that the region bounded by the curves, y is equal to 4 e power minus x, y is equal to 4 and x equal to 2 about y is equal to 8.
00:22
We need to find the volume of the solid.
00:26
For that, equating 4e power minus x which is equal to 4, which implies, e power minus x which is equal to 1, taking lawn on both sides, we get minus x which is equal to 0, x equal to 0.
00:42
Therefore, x varies from 0 to 2.
00:48
Then the volume of the solid is v, which is equal to integral 0 to 2, pi into, the function is 4e power minus x minus 8 the square.
01:11
Minus 4 the square into d x which is equal to here pi is constant taking out pi we get integral over 0 to 2 16 e power minus 2 x plus 64 minus 64 e power minus x minus 16 into d x which is equal to pi into integral over 0 to 2 simplifying this we get 16 e power minus 2 x minus 64 e power minus x plus 48 into d x now integrating the function with respect to x, we get pi into 16 into e power minus 2x divided by minus 2, minus 64 into e power minus x divided by minus 1 plus 48x over the interval 0 to 2...