💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



Problem 39 Hard Difficulty

First make a substitution and then use integration by parts to evaluate the integral.

$ \displaystyle \int_{\sqrt{\frac{\pi}{2}}}^{\sqrt{\pi}} \theta^3 \cos (\theta^2) d \theta $


$\frac{1}{2}(\pi \sin \pi+\cos \pi)-\frac{1}{2}\left(\frac{\pi}{2} \sin \frac{\pi}{2}+\cos \frac{\pi}{2}\right)=\frac{1}{2}(\pi \cdot 0-1)-\frac{1}{2}\left(\frac{\pi}{2} \cdot 1+0\right)=-\frac{1}{2}-\frac{\pi}{4}$


You must be signed in to discuss.

Video Transcript

The problem is first maker substitution on DH. Then use integration. My parts Teo Why, I'd have been to grow so faint. Signal is into girl from return of pie over to two Frito Pie. The disco fits Q times consign clear the square. The first I can use use of prostitution. But they go to data squad, then the US is the ax too. Two times you stay there. Now this integral is you called too into girl from high over two to pie. The square is facts on the deep has one half the axe and assign Get square is consign Since this integral is factual into peril from pie or two to pine one half times Max um school sign axe. Now this is Carter would have Here is one half times pi work to pie. Sykes, Jax. Now we can use integration. My pass. So the formula is into girl from a to B you be prime the axe. It's the call to you have sleeve from a B minus in general, from a to B your prime housefly axe. Oh, our problem. We can let you is equal to x and they re prom is recalled to assign Max. Then you prom is equal to one. Read it. Sign acts now this into your office. Hans Newtown Suiza, this is X Hammes Sign. Thanks from hi over to two. Minus into your own. Your prime time squeezes. This is Sign Axe from high work. You too. Hi. I think so too. My half first term. This zero minus pi over two and interior ofthe sign Axe is negative. Kasai Axe, This's class Sign Max from high over to too high. This is one half. I'm selective pie. Over two. They assign highs. Makes you want fine power to zero, which is the answer is half half snaked. Your power too minus one.