Saturday
August 2, 2014

Homework Help: Math

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

a) Is ∫[-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 < ∫[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

First Name:
School Subject:
Answer:

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 x2 always positive, always ...
Math - Could someone please explain to me how you get answers when you add a ...
Chemistry(Please check answers) - 1) For a reaction delta Go is more negative ...
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 ...

Search
Members