Evaluate the integral.

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


Evaluate the integral.

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

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:

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Given Data

  • The given definite integral is {eq}\displaystyle \int\limits_0^{\dfrac{\pi }{2}} {{{\cos }^2}\theta } d\theta {/eq}.

Solving the given...

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Learn more about this topic:

Definite Integrals: Definition


Chapter 12 / Lesson 6

A definite integral is found as the limit between a line graphed from an equation, and the x-axis, either positive or negative. Learn how this limit is identified in practical examples of definite integrals.

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