Question

integration of cos2xdx from 0 to pi/4​

Answer 1

$\displaystyle \sf \int\limits_{0}^{ \frac{\pi}{4} } cos \: 2x \, dx = \frac{1}{2}$

Given :

$\displaystyle \sf \int\limits_{0}^{ \frac{\pi}{4} } cos \: 2x \, dx$

To find :

Integrate the integral

Solution :

Step 1 of 2 :

Write down the given Integral

Here the given Integral is

$\displaystyle \sf \int\limits_{0}^{ \frac{\pi}{4} } cos \: 2x \, dx$

Step 2 of 2 :

Integrate the integral

$\displaystyle \sf \int\limits_{0}^{ \frac{\pi}{4} } cos \: 2x \, dx$

$\displaystyle \sf{ = \frac{sin \: 2x}{2} \bigg|_ {0}^{ \frac{\pi}{4} } }$

$\displaystyle \sf{ = } \frac{1}{2} \times \bigg[ sin \: 2x\bigg] _ {0}^{ \frac{\pi}{4} }$

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ sin \: \frac{\pi}{2} - sin \: 0\bigg] }$

$\displaystyle \sf{ = \frac{1}{2} \times \bigg[ 1 - 0\bigg] }$

$\displaystyle \sf{ = \frac{1}{2} }$

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Answer 2

Answer:

The integration of $\int_{0}^{\frac{\pi}{4}} \cos 2 x d x$ is $=\frac{1}{2}$.

Explanation:

Integration exists in the computation of an integral. Integrals in maths are used to discover many useful portions such as areas, volumes, displacement, etc.

Integration exists utilized to add large values in mathematics when the measures cannot be performed on general procedures.

Given,

$\int_{0}^{\frac{\pi}{4}} \cos 2 x d x=\frac{1}{2}$

To find,

The integration of $\int_{0}^{\frac{\pi}{4}} \cos 2 x d x=\frac{1}{2}$.

Step 1 of 1

Integrate the integral.

Here the provided Integral is,

$\int_{0}^{\frac{\pi}{4}} \cos 2 x d x$

Integrate the integral

$\int_{0}^{\frac{\pi}{4}} \cos 2 x d x$

$=\left.\frac{\sin 2 x}{2}\right|_{0} ^{\frac{\pi}{4}}$

$=\frac{1}{2} \times[\sin 2 \times]_{0}^{\frac{\pi}{4}}$

$=\frac{1}{2} \times\left[\sin \frac{\pi}{2}-\sin 0\right]$

Simplifying the values of the above equation,

$=\frac{1}{2} \times[1-0]$

Hence,

$=\frac{1}{2}$.

Therefore, the integration of $\int_{0}^{\frac{\pi}{4}} \cos 2 x d x=\frac{1}{2}$.

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