Definite Integrals

Express each limit as a definite integral. Then evaluate the integral to find the value of the limit. In each case, P is a partition of the given interval and the numbers ck are chosen from the subintervals of P

where P is a partition of [1, 5]

Solution:-

Step 1 of 3</p>

Given that

We have to express the limit as a definite integral and we have to evaluate the integral to find the value of the limit.

Step 2 of 3</p>

We have

where P is a partition of [1, 5]

Clearly, the lower limit is and the upper limit is and in Riemann sums, the function is

So, we get

So, the integral is

Therefore, the limit as definite integral is