How do I evaluate #int_(5pi\/4)^(4pi\/3)10 sec(theta) tan(theta) d theta#?
Try this:
By signing up, you agree to our Terms of Service and Privacy Policy
To evaluate ( \int_{\frac{5\pi}{4}}^{\frac{4\pi}{3}} 10 \sec(\theta) \tan(\theta) , d\theta ), we can use the fact that ( \sec(\theta) ) is the reciprocal of ( \cos(\theta) ) and ( \tan(\theta) ) is the ratio of ( \sin(\theta) ) to ( \cos(\theta) ).
So, ( \sec(\theta) \tan(\theta) = \frac{\sin(\theta)}{\cos^2(\theta)} ).
Now, integrate ( \frac{\sin(\theta)}{\cos^2(\theta)} ) with respect to ( \theta ) over the given interval ([ \frac{5\pi}{4}, \frac{4\pi}{3} ]).
After integrating, substitute the upper and lower limits of integration and subtract the result obtained at the lower limit from the result obtained at the upper limit to find the final answer.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you integrate #int sec^3xtanx#?
- How do you find the integral of #f(x)=x^2sinx# using integration by parts?
- How do you integrate #int cos^3(x/3)dx#?
- How do you integrate #int (3x-2x^2)/((x+9)(x+7)(x+1)) # using partial fractions?
- How do you integrate #int x^3 cos^2x 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