 Hi and welcome to the session. I am Purva and I will help you with the following question. Find the area under the given curve and given line y is equal to x raised to the power 4, x is equal to 1, x is equal to 5 and x axis. Now the area of the region enclosed between y is equal to fx, x is equal to a, x is equal to b and x axis is given by integral, limit is from a to b, fx, dx. So the area of the region enclosed between the curve y is equal to fx and the lines x is equal to a and x is equal to b and x axis is given by integral limit from a to b, fx, dx. So this is the key idea which we will use to solve this question. Now we pick in with the solution. Now y is equal to x raised to the power 4 is a curve with vertex at 0, 0 and symmetric about y axis. So here we get a curve y is equal to x raised to the power 4 with vertex at 0, 0 and it is symmetric about y axis and x is equal to 1 and x is equal to 5 are the two lines which are parallel to y axis. Thus this shaded region bounded by the curve y is equal to x raised to the power 4, x axis and the lines x is equal to 1 and x is equal to 5 is the region whose area is to be found out. Therefore required area is equal to, now by key idea we can clearly see that in our question we have fx is equal to x raised to the power 4, a is equal to 1 and b is equal to 5. So we have required area is equal to integral limit from a to b that is from 1 to 5 fx dx. Now here fx is equal to x raised to the power 4 dx. This is equal to now integrating x raised to the power 4 we get x raised to the power 5 upon 5 and limit is from 1 to 5. This is equal to now putting the limits we get 5 raised to the power 5 upon 5 minus 1 by 5 and this is further equal to now 5 raised to the power 5 is equal to 3125 upon 5 minus 1 by 5 and this is equal to now 3125 minus 1 is 3124 upon 5 and we get this is equal to 624.8. So we get our required area as 624.8. Hence the required area is equal to 624.8. So this is our answer. Hope you have understood the solution. Take care and God bless you.