# Math Physics Tricky Integrals go Over my Head

• dazednconfuze
In summary, the conversation revolves around a problem involving the integral ∫ u2 (1-u2)3/2 du, from u = 0 to u = 1 and whether to use trig substitution or integration by parts to solve it. The suggestion is to use u = sin(theta) and apply trig identities.
dazednconfuze
so i have this question about a ladder and the area under it and when it all comes down to it I get the integral, ∫ u2 ( 1 – u2 ) 3/2 du, from u = 0 to u = 1.

I am not sure whether to use trig substitution. I keep ending up in the same boat when I do. . . And the same thing when I do integration by parts. I'm not too quick with integration obviously. any help?

is u2 u*2?

I'm almost going to have to guess it's u*(1-u)^(-3/2) that's giving you trouble(or 2*u or whatever)

in which case I think integration by parts will do it

What's the actual problem though?

I assume you mean $$\int_0^1 u^2(1-u^2)^{3/2} du$$.
Let $$u=\sin\theta$$ and brush up on your trig.
Use the formulae for sin and cos of theta/2.

oh ok, that makes more sense with what he typed >_>

You'll need those trig identities, but you can find huge tables of such identities in moments courtesy of the internet

I tried substituting u = sin(theta) and all I got was sin^2(theta) cos^4(theta) dtheta... and that just doesn't mean anything to me...

$$\int \sin^2 \theta {} \cos^4 \theta {} {} d\theta = \frac{1}{4}\int \sin^2 2\theta \ \frac{1+\cos 2\theta}{2} {} d\theta$$

Can you carry on from here ?

## 1. What is the difference between math and physics?

Math is a branch of science that deals with numbers, quantities, and shapes. It is used to solve problems and make predictions. Physics, on the other hand, is a branch of science that deals with the study of matter, energy, and their interactions. It uses mathematical equations to describe and explain natural phenomena.

## 2. What is the purpose of studying math and physics together?

Studying math and physics together helps us understand the fundamental laws and principles that govern the natural world. It also allows us to make accurate predictions and solve complex problems.

## 3. Why are integrals considered tricky in math physics?

Integrals are tricky in math physics because they involve finding the area under a curve, which can be difficult to visualize. They also require a deep understanding of both math and physics concepts, making them challenging to solve.

## 4. How can I improve my skills in solving tricky integrals?

To improve your skills in solving tricky integrals, it is important to have a strong foundation in both math and physics. Practice regularly and familiarize yourself with different integration techniques. It also helps to break down the problem into smaller, more manageable steps.

## 5. Are there any real-life applications of tricky integrals in math physics?

Yes, there are many real-life applications of tricky integrals in math physics. They are used to calculate the trajectory of a projectile, determine the amount of work done by a force, and even in designing bridges and buildings. They are essential in understanding and predicting natural phenomena in the real world.

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