Find each of the following integrals:∫ 1√9 − x2 dx
Question
Find each of the following integrals:∫ 1√9 − x2 dx
Solution
The integral you're asking about is a standard form of inverse trigonometric integral. Here's how to solve it:
∫ 1/√(9 - x²) dx
This is a standard form of integral that is recognized as:
∫ dx/√(a² - x²) = arcsin(x/a) + C
where a is a constant and C is the constant of integration.
In your case, a = √9 = 3. So, the integral becomes:
= arcsin(x/3) + C
So, ∫ 1/√(9 - x²) dx = arcsin(x/3) + C.
Similar Questions
Evaluate the following integrals.(b)∫ 21xe3x dx (c)∫ cos(√x)√x dx (d)∫ x2 + 3x + 3x + 1 dx
Evaluate the following definite integral:∫91𝑥‾‾√ d𝑥=
1. Evaluate the following integrals a. ∫ √𝑥𝑑�
Find the following indefinite integral: (√x-2ex+9x)dx ○x²-2x+63x²+c 3 3 2 9 -2ex+x+c 7 ○x²-20*+63x²+c 2e 7 3 97 x²-2x+x+c
Express the following integrals in terms of gamma function(1) ∫ 𝑑𝑥√1;𝑥410 (2) ∫ √cot 𝜃 𝑑𝜃
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.