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Solve the given problems by integration.Find the area under the curve $y=\sin x$ from $x=0$ to $x=\pi$
Calculus 1 / AB
Chapter 28
Methods of Integration
Section 4
Basic Trigonometric Forms
Integrals
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Lectures
03:09
In mathematics, precalculu…
31:55
In mathematics, a function…
01:58
Evaluate the following int…
02:20
Find the area of the regio…
04:28
Find the area under the cu…
01:16
For the following exercise…
01:05
02:08
Use basic integration form…
05:32
Use a definite integral to…
01:00
Write the given (total) ar…
03:05
Sketch the curve and find …
04:12
Evaluate the integrals.
in this question we want to find the area under the curve of why equals to sine X from X equals 02 X equals two pi. No Sign X will look like that from 0 to Pi. And if we were to just take a small slice like this that we've been very small. So we're quite delta X. R. D. X. Now over here would be the white value of this slice. So for these lines the area will be Y the X. But now we will be adding all the areas of this little slice from X equals 02 S. Costa pie. Now since this is a continuous submission it will be the integration sign from S. Equals zero to S. Equals two pi. So this one will be the area underground. Okay so for area underground we will have zero to pi Y. D. X. And this will be my wife is Sine X. The X. Now we know that when we integrate Sine X will get co sign X with a minus. And since this is the definite integral we had a lower living or zero and upper limit of time. So let me put the minus side outside to co sign X. Like that within the the square break it here. So we have minus cosine pi minus Co sign zero and this will be right minus now frozen. Pie is minus one minus cosine zero is one, so we will have two units square. Mhm.
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