 Hi friends, I am Purva and today I will help you with the following question. Choose the correct answer in the following. Question is area bounded by the curve y is equal to x cube, the x axis and the ordinate x is equal to minus 2 and x is equal to 1 is a minus 9 b minus 15 upon 4 c 15 upon 4 d 17 upon 4. Let us now begin with the solution. Now here we have to find the area bounded by the curve y is equal to x cube, the x axis and x is equal to minus 2 and x is equal to 1. For identifying the region, let us draw a rough sketch of the curve y is equal to x cube. Now for positive values, this curve passes through 0, 0, 1, 1, 2, 8 and so on. If we take negative values of x then the curve passes through minus 1, minus 2, minus 8 and so on. Thus one part of the curve lies in the first quadrant and the other in the third quadrant. Also x is equal to minus 2 and x is equal to 1, our line is parallel to y axis. So this is the curve y is equal to x cube, this is the line x is equal to 1 and this is the line x is equal to minus 2 and we have to find the area of this shaded region. Now here we shall remember that we will take the absolute value of the area of the region below x axis. Therefore required area is equal to modulus of integral limit from minus 2 to 0, x cube dx plus integral limit from 0 to 1, x cube dx. And this is equal to modulus of, now integral x cube is equal to x 4 upon 4 and here we have limit is from minus 2 to 0 plus integral x cube is equal to x 4 upon 4 and here we have limit is from 0 to 1. This is equal to modulus of 1 upon 4, now putting the limits we get 0 minus 16, putting upper limit 0 in place of x we get 0 minus putting lower limit minus 2 in place of x we get 16 plus again putting the limits we get 1 upon 4 minus 0 and this is equal to modulus of now 0 minus 16 is minus 16 upon 4 plus 1 upon 4 minus 0 is 1 upon 4. Canceling the common factor 4 we get 4 in numerator, so we have this is equal to now modulus of minus 4 is equal to 4 plus 1 upon 4 and this is equal to 17 upon 4 and this is same as d part, hence the correct answer is d. Hope you have understood the solution bye and take care.