## Integration of cube root of x | Integral of cube root of x

The cube root of x is a number whose cube is x, in other words, (cube root of x)^3 = x. In this post, we will evaluate the integration of the cube root of x. To do so, we will use the power rule of derivatives which is given below: $\int x^n dx = \dfrac{x^{n+1}}{n+1}+c$ … Read more

## Integration of square root of x | Integral of 1 by root x

The integration of root x is equal to 2/3 x3/2+C. In this post, we will calculate the integration of the square root of x. Note that the square root of x is an algebraic function. We will use the following power rule of derivatives: $\int x^n dx = \dfrac{x^{n+1}}{n+1}+c$ $\cdots (i)$ where $c$ is … Read more

## Solved Problems Using Definition of Definite Integrals

Here we solve few problems of definite integrals. Problem 1:  By the definition of definite integrals, find int_a^b dx. Solution: From the definition of definite integrals, we have int_a^b dx=lim_{h to 0} h sum_{1}^{n} 1, quad where  nh=b-a             =lim_{h to 0} h (1+1+1+ cdots text{till} n text{-terms})             `=lim_{h … Read more