Integration of 1/2 sin y dy from 0 to pi/2: Solution

In summary, the integration of 1/2 sin y dy from 0 to pi/2 is equal to 1/2. This is because the integration of sin y is equal to -cos y, and when evaluated from 0 to pi/2, the result is 1/2 [-cos (pi/2) - (-cos 0)], which simplifies to 1/2 [0 + 1] or 1/2. It is important to make sure your calculator is in the correct mode (radians versus degrees) when solving these types of problems.
  • #1
ilikeicetea
4
0

Homework Statement


what is the integration of 1/2 sin y dy from 0 to pie/2


Homework Equations


i know sin y = -cos y (integration)



The Attempt at a Solution


from 1/2 sin y dy to (1/2) -cos y then i plot pie/2 and 0
i got (1/2) [-cos (pie/2) - (-cos 0)] = 0, but the answer is 1/2
i mean -cos (pie/2) = -1 & cos 0 = 1

Thank you for helping
 
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  • #2
ilikeicetea said:

Homework Statement


what is the integration of 1/2 sin y dy from 0 to pie/2


Homework Equations


i know sin y = -cos y (integration)



The Attempt at a Solution


from 1/2 sin y dy to (1/2) -cos y then i plot pie/2 and 0
Error in next line. BTW, the name of the Greek letter is pi, not pie. Pie is something you can eat.
(1/2)[-cos (pi/2) - (-cos 0)] != 0
ilikeicetea said:
i got (1/2) [-cos (pie/2) - (-cos 0)] = 0, but the answer is 1/2
i mean -cos (pie/2) = -1 & cos 0 = 1

Thank you for helping
 
  • #3
i forgot to add this, I am trying to find out why the answer is 1/2 and not 0.
 
  • #4
See post 2. I identified the line where you went wrong.
 
  • #5
but i though the integration of sin y is -cos y?
 
  • #6
I'm not questioning that. Did you read post 2?
 
  • #7
integration of 1/2sin(y) dy from 0 to pie/2=1/2[-cos(y)] from 0 to pie/2
=1/2{-cos(pie/2)-[-cos(0)]}
=1/2{0+1}
=1/2 [bcoz cos(0)=1 & cos(pie/2)=0]



:smile:
 
  • #8
k, i got it, i put cos (pi/2) in my calculator but came out to be .9996, so that's why i didn't get the right answer.

edit. just know why, cause i have the mode under deg so that's why my answer is all mess up.

thanks everybody
 

What is the formula for integrating 1/2 sin y dy from 0 to pi/2?

The formula for integrating 1/2 sin y dy from 0 to pi/2 is ∫ 1/2 sin y dy = (1/2) ∫ sin y dy = (1/2) (-cos y) + C = -1/2 cos y + C.

Why is the solution for integrating 1/2 sin y dy from 0 to pi/2 negative?

The solution for integrating 1/2 sin y dy from 0 to pi/2 is negative because the integral of sin y is -cos y and the constant term C is also negative. This results in a negative overall solution.

How is the integral of 1/2 sin y dy from 0 to pi/2 related to the area under the curve?

The integral of 1/2 sin y dy from 0 to pi/2 represents the area under the curve of the function f(y) = 1/2 sin y from y = 0 to y = pi/2. This is because the integral is essentially finding the sum of infinitely small rectangles under the curve, which approximates the area under the curve.

Can the solution for integrating 1/2 sin y dy from 0 to pi/2 be simplified further?

Yes, the solution for integrating 1/2 sin y dy from 0 to pi/2 can be simplified further using trigonometric identities. For example, -1/2 cos (pi/2) + C = -1/2 * 0 + C = C. Therefore, the final solution can be written as -1/2 cos y + C = C.

What are the units of the solution for integrating 1/2 sin y dy from 0 to pi/2?

The units of the solution for integrating 1/2 sin y dy from 0 to pi/2 are determined by the units of the variable y. For example, if y is in radians, then the units of the solution would be in radians. If y is in degrees, then the units of the solution would be in degrees.

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