University:
Stanford University
Course:
MATH 52 | Integral Calculus of Several Variables
Academic year:

2023
Views:

15

Pages:

23
Author:

MathPaladin

Questions and Answers Sheet 7 Applications of Integrals Applications of Integrals Question #1 Find the indefinite integral. cos 𝑡 ∫ 𝑑𝑡 1 + sin 𝑡 Answer: Let's find Question #2 Find integral. ∫ tan 7 𝑥𝑑𝑥 Answer: See my solution: Question #3 Evaluate the integral. 2 (𝑥+1)2 ∫1 𝑥 𝑑𝑥 Answer: Question #4 Evaluate the following integrals. 𝑥+4 ∫ 2 𝑑𝑥 𝑥 + 8𝑥 + 25 Answer: Explanation is given below Question #5 Evaluate the following iterated integrals. 𝑒 1 ∫ ∫ 4(𝑝 + 𝑞) ln 𝑞 𝑑𝑝 𝑑𝑞 1 0 Answer: Right answer: Question #6 Determine the following indefinite integral. Check your work by differentiation. ∫ sin 0−1 cos2 0 𝑑0 Answer: Let's determine: Question #7 Evaluate the following integral. ∫ cos 𝑥 [cos(sin 𝑥)]𝑑𝑥 Answer: I have written answer for you: Question #8 Find the indefinite integral. ∫(5 cos 𝑥 − 2 sec 2 𝑥)𝑑𝑥 Answer: Finding of explanation is given below Question #9 Evaluate the following integrals. Include absolute values only when needed. 𝑒 5+√𝑥 ∫ 𝑑𝑥 √𝑥 Answer: Your solution: Question #10 Evaluate the definite integral. 4 𝑥2 ∫ (3𝑥 − ) 𝑑𝑥 4 0 Answer: Evaluating Question #11 Evaluate the definite integral. 1 ∫ (√3𝑥 − 2)𝑑𝑥 −1 Answer: Answer is on photo Question #12 Determine the following indefinite integral. 2𝑒 2𝑥 + 𝑒 𝑥 ∫ 𝑑𝑥 𝑒𝑥 Answer: So, let's determine: Question #13 Find integral. ∫ √cos 𝑥 sin 𝑥 𝑑𝑥 Answer: Your integral: Question #14 Find the indefinite integral. 𝑥 2 + 4𝑥 ∫ 3 𝑑𝑥 𝑥 + 6𝑥 2 + 5 Answer: Try to use my answer: Question #15 Find the indefinite integral 2 ∫ 𝑥(5−𝑥 )𝑑𝑥 Answer: Le's find this integral Question #16 Evaluate the integral. ∫ cos 𝑥 sin 𝑥 Answer: Answer is given on photo Question #17 Determine whether each integral is convergent ordivergent. Evaluate those that are convergent integral 0 to 1 (1 − 𝑥 2 )(4𝑥 − 9)𝑑𝑥 Answer: Explanation is givwn below: Question #18 Find the indefinite integral. ∫ cos 2 3𝑥𝑑𝑥 Answer: Integration Question #19 Determine the following indefinite integral. ∫ 𝑦 3 −9𝑦 2 +20𝑦 𝑦−4 𝑑𝑦 Answer: See my photo for answer Question #20 Evaluate the following integrals. Include absolute values only when needed. ∫ 𝜋 2 0 sin 𝑥 𝑑𝑥 1 + cos 𝑥 Answer: Hope, it will help you