Math  /  Calculus

Question21. Find 11xdx\int_{1}^{\infty} \frac{1}{x} \mathrm{dx}. a) 0 c) -\infty b) 1 d) \infty
22. Find 12x3dx\int_{1}^{\infty} \frac{2}{x^{3}} d x. a) 0 c) 2 b) 1 d) \infty
23. Find 0414xdx\int_{0}^{4} \frac{1}{\sqrt{4-x}} d x. a) -4 b) 0 c) 4 d) does not exist.

Studdy Solution
Take the limit as t4 t \to 4^- :
limt4(24t+4)=2(0)+4=4 \lim_{t \to 4^-} \left( -2\sqrt{4-t} + 4 \right) = -2(0) + 4 = 4
Since the limit is finite, the integral converges.
The answer for problem 23 is: 4\boxed{4}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord