# What is #f(x) = int xcotx^2 dx# if #f((5pi)/4) = 0 #?

I have tried , but it is complicated for

Here,

So,

Given that,

Now,

#(25xxpi^2)/16 ~~15.42....#

Thus,

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

To find ( f(x) = \int x \cot(x^2) , dx ) when ( f \left( \frac{5\pi}{4} \right) = 0 ), we first differentiate ( f(x) ) using the fundamental theorem of calculus and apply the given condition to solve for the constant of integration.

Differentiating ( f(x) ), we get:

[ f'(x) = \cot(x^2) - 2x^2 \csc^2(x^2) ]

Given ( f \left( \frac{5\pi}{4} \right) = 0 ), we substitute ( x = \frac{5\pi}{4} ) into ( f(x) ):

[ \int_{0}^{\frac{5\pi}{4}} x \cot(x^2) , dx = 0 ]

[ \left[ -\frac{1}{2} \csc(x^2) \right]_0^{\frac{5\pi}{4}} = 0 ]

[ -\frac{1}{2} \csc \left(\frac{25\pi^2}{16}\right) + \frac{1}{2} \csc(0) = 0 ]

[ -\frac{1}{2} \csc \left(\frac{25\pi^2}{16}\right) = -\frac{1}{2} \csc(0) ]

[ \csc \left(\frac{25\pi^2}{16}\right) = \csc(0) ]

Since ( \csc(0) ) is undefined, there might be an error in the given problem or the function ( f(x) ) might not satisfy the conditions stated.

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.

- How do you integrate #(e^x)(cosx) dx#?
- How do you use partial fractions to find the integral #int (sinx)/(cosx+cos^2x)dx#?
- How do you use Integration by Substitution to find #intx^2*sqrt(x^3+1)dx#?
- How do you integrate #int(x+1)/((6x^2+4)(x-5))# using partial fractions?
- What is #f(x) = int x-sin2x+cosx dx# if #f(pi/2)=3 #?

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