# How do I evaluate the integral: #int_0^(7sqrt(3/2))dx / sqrt(49-x^2)#?

First, recall the antiderivative formula:

Thus,

We have

Substitute in the constraints we

Please find the formula sheet below for reference:

By signing up, you agree to our Terms of Service and Privacy Policy

To evaluate the integral ( \int_0^{7\sqrt{\frac{3}{2}}} \frac{dx}{\sqrt{49-x^2}} ), we can use trigonometric substitution. Let ( x = 7\sin(\theta) ), then ( dx = 7\cos(\theta)d\theta ).

Substituting these into the integral, we get:

[ \int_0^{\frac{\pi}{2}} \frac{7\cos(\theta)d\theta}{\sqrt{49 - 49\sin^2(\theta)}} ]

[ = \int_0^{\frac{\pi}{2}} \frac{7\cos(\theta)d\theta}{\sqrt{49\cos^2(\theta)}} ]

[ = \int_0^{\frac{\pi}{2}} \frac{7\cos(\theta)d\theta}{7\cos(\theta)} ]

[ = \int_0^{\frac{\pi}{2}} d\theta ]

[ = \left[\theta\right]_0^{\frac{\pi}{2}} ]

[ = \frac{\pi}{2} ]

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you integrate #int 1/sqrt(x^2-16x+37) # using trigonometric substitution?
- How do you integrate #int4sec4x*tan4x*sec^4 4x# using substitution?
- What is #f(x) = int xe^x-xsqrt(x^2+2)dx# if #f(0)=-2 #?
- How do you integrate #int x/(x-6) dx# using partial fractions?
- How do you integrate #int x^3 e^(x^2 ) dx # using integration by parts?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7