Evaluate the integral.

{eq}\displaystyle \int_{0}^{\frac{\pi}{2}} \cos^2 \theta d \theta {/eq}

Question:

Definite and Indefinite Integral:

There are two types of integral based on the boundary's values (upper and lower limits).

1) Definite integral (A definite integral came with the boundaries values)

2) Indefinite integral (An indefinite integral does not have the boundaries values)

The following formula can be used to find the solution of the given definite integral.

$$\begin{align*} \int {ay\left( x \right)} dx &= a\int {y\left( x \right)} dx\\[0.3cm] \int 1 dx &= x + C\\[0.3cm] \int {\cos \left( {ax} \right)} dx &= \dfrac{{\sin \left( {ax} \right)}}{a} + C \end{align*} $$

Here, {eq}a {/eq} is a constant value.

Answer and Explanation: