Find the Integral

Calculus Level 2

$\large \int_0^\frac \pi 2 \cos x \sqrt{\sin x+1}\ dx =\ ?$

The answer is 1.2190.

1 solution

Chew-Seong Cheong
Mar 26, 2020

$\begin{aligned} I & = \int_0^\frac \pi 2 \cos x \sqrt{\sin x +1}\ dx & \small \blue{\text{Let }u = \sin x \implies du = \cos x \ dx} \\ & = \int_0^1 \sqrt{u+1} \ du \\ & = \frac 23 (u+1)^\frac 32 \ \bigg|_0^1 \\ & = \frac 23 \left(2\sqrt 2 - 1\right) \\ & \approx \boxed{1.22} \end{aligned}$

@Aly Ahmed , why don't you learn how to use LaTex? The above equation is $\backslash$ [\int_0^\frac \pi 2 \cos x \sqrt{\sin x +1} dx = ? $\backslash$ ].

Chew-Seong Cheong - 1 year, 2 months ago

sir chew seong how can i add an imge of the answer plz

Aly Ahmed - 1 year, 2 months ago

Add an image, by clicking on the image icon on the "Add your own explanation" section.

Nikola Alfredi - 1 year, 2 months ago

thank you very much sir chew seong bbut iwrite from my mobile

Aly Ahmed - 1 year, 2 months ago

You can still key in with a mobile. Just add $\backslash$ ( and (\backslash)) and the rest. I sometimes give solution through my mobile.

Chew-Seong Cheong - 1 year, 2 months ago

Find the Integral

The answer is 1.2190.

1 solution

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