Posted by **Rain** on Sunday, September 10, 2006 at 1:45am.

a) Is âˆ«[-1 to 1]e^x^3 dx positive, negative, or zero? Explain.

I think is positive but i don't know how to explain it.

b) Explain why 0 < âˆ«[0 to 1] e^x^2 dx <3.

Can you type this equation or whatever in a better format? What branch of math does this problem come from?

Rachel

It's definitely a calculus problem, but some of the symbols didn't translate to ASCII. You'll need to give a brief description of the problem for the symbols you can't type.

Is a) the integral of e^(x^3)dx? on the interval [-1,1]? If so, then you should see that the function is positive on that interval, thus the area is positive.

Part b) appears to put a bound on the definite integral e^(x^2) on the interval [0,1]. f(x)=e^(x^2) is a monotonic increasing funtion on R, has a min of 1 on that interval, and a max of e on that interval The area is <=e<3, and the area is positive since the function is positive there. Thus 0<f(x)<3 for x in [0,1]

After checking my work I see I stated the function for b) wrong. f(x) is monotonic increasing on the interval [0,1], not on R.

Both problems are asking you to make determinations about the area of some exponential function. In b) e^(x^2) is symmetric about the x-axis, but it's increasing on the interval [0,1]. To see this, simply differentiate the function and you'll see it's slope is increasing at every point there.

## Answer this Question

## Related Questions

- Decartes Rule of Signs - Could you explain to me decartes Rule of signs? Here ...
- Algebra - Tell whether the sum is positive, negative, or zero. Explain n is ...
- Algebra - Tell whether the sum is positive, negative, or zero. Explain n is ...
- phsics - throughout a time interval, while the speed of a particle increases as ...
- algebra - Could someone please help me with this? (1) If x is a nonzero real ...
- algebra - ) If x is a nonzero real number, is x–2 always positive, always ...
- Chemistry(Please check answers) - 1) For a reaction delta Go is more negative ...
- Math - Could someone please explain to me how you get answers when you add a ...
- Physics(Please check) - There is a PV diagram with ABC and the cycle is moving ...
- math-calculus - write the following absolute value functions as piecewise ...