# What is the integral of #int (sin2x)/sinx #?

By signing up, you agree to our Terms of Service and Privacy Policy

The integral of (\int \frac{\sin(2x)}{\sin(x)} , dx) is (-2\ln|\csc(x) + \cot(x)| + C), where (C) is the constant of integration.

By signing up, you agree to our Terms of Service and Privacy Policy

To find the integral of (\frac{\sin(2x)}{\sin(x)}), we can use the following steps:

- Rewrite the numerator using the double angle identity: (\sin(2x) = 2\sin(x)\cos(x)).
- Rewrite the integral as: (\int \frac{2\sin(x)\cos(x)}{\sin(x)} , dx).
- Cancel out the (\sin(x)) term in the denominator.
- Integrate (\cos(x)) with respect to (x).

Following these steps, the integral becomes:

[\int 2\cos(x) , dx]

The integral of (\cos(x)) is (\sin(x)) (plus a constant), so integrating (2\cos(x)) with respect to (x) gives:

[2\sin(x) + C]

Where (C) is the constant of integration. Therefore, the integral of (\frac{\sin(2x)}{\sin(x)}) with respect to (x) is (2\sin(x) + C).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What's the area of the first quadrant region bounded by the y-axis, the line #y=4-x # and the graph of #y=x-cosx#?
- How do you find the integral of #int (cotx)^5(sinx)^4dx#?
- How do you find the integral of #cos^n x #?
- How do you calculate the double integral of #f(x,y) = 28y(e^x)# over the triangle indicated by the following points (0,0), (4,1), and (4,3)?
- How do you evaluate #int x^2 + x + 4dx# for [0, 2]?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7