# How do you find the area under the graph of #f(x)=e^(-2lnx)# on the interval [1, 2]?

Thus the area under the curve is

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

To find the area under the graph of ( f(x) = e^{-2 \ln x} ) on the interval [1, 2], you need to integrate the function over that interval. First, rewrite the function in terms of ( x ) to simplify it: ( e^{-2 \ln x} = e^{\ln x^{-2}} = x^{-2} ). Now, integrate ( x^{-2} ) from 1 to 2 with respect to ( x ).

[ \int_{1}^{2} x^{-2} , dx = \left[ -x^{-1} \right]_{1}^{2} = -\frac{1}{2} + \frac{1}{1} = \frac{1}{2} ]

So, the area under the graph of ( f(x) = e^{-2 \ln x} ) on the interval [1, 2] is ( \frac{1}{2} ).

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.

- How do you use the properties of summation to evaluate the sum of #Sigma (i^3-2i)# from i=1 to 15?
- What is #int (-x^3-2x-3 ) / (7x^4+ 5 x -1 )#?
- What is the antiderivative of #(sqrt(1 + sqrt((1+sqrt(x)))dx#?
- What is the antiderivative of #3/x#?
- How do you evaluate the definite integral by the limit definition given #int 4dx# from [0,3]?

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