Best Answer

First we look at the double-angle identity of cos2x.

We know that:

cos2x = cos^2x - sin^2x

cos2x = [1-sin^2x] - sin^2x.............. (From sin^2x + cos^2x = 1, cos^2x = 1 - sin^2x)

Therefore:

cos2x = 1 - 2sin^2x

2sin^2x = 1 - cos2x

sin^2x = 1/2(1-cos2x)

sin^2x = 1/2 - cos2x/2

And intergrating, we get:

x/2 - sin2x/4 + c...................(Integral of cos2x = 1/2sin2x; and c is a constant)

Study guides

☆☆

Q: Integral of sin squared x

Write your answer...

Submit

Still have questions?

Continue Learning about Calculus

Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).

The integral of x cos(x) dx is cos(x) + x sin(x) + C

arctan(x)

The integral of cot(x)dx is ln|sin(x)| + C

∫ cot(x) dx is written as: ∫ cos(x) / sin(x) dx Let u = sin(x). Then, du = cos(x) dx, giving us: ∫ 1/u du So the integral of 1/u is ln|u|. So the answer is ln|sin(x)| + c

Related questions

.5(x-sin(x)cos(x))+c

Integral of [1/(sin x cos x) dx] (substitute sin2 x + cos2 x for 1)= Integral of [(sin2 x + cos2 x)/(sin x cos x) dx]= Integral of [sin2 x/(sin x cos x) dx] + Integral of [cos2 x/(sin x cos x) dx]= Integral of (sin x/cos x dx) + Integral of (cos x/sin x dx)= Integral of tan x dx + Integral of cot x dx= ln |sec x| + ln |sin x| + C

sin integral is -cos This is so because the derivative of cos x = -sin x

Sin squared, cos squared...you removed the x in the equation.

Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).

-cotan(x)

integral of radical sinx

âˆ« sin(x)/cos2(x) dx = sec(x) + C C is the constant of integration.

-cos x + Constant

No.

sin2x + c

The integral of x cos(x) dx is cos(x) + x sin(x) + C

People also asked