# Calculus

posted by .

My book says to do the following problem via computer and via hand:

Calculate the definite Integral of
e^-x * cos x dx
over (0, +infinity)

My TI-89 calculator gets 1 (it gets the same thing when I replace infinity with 999).

when I do this by hand, I get: 1/2.

The formula e^-x * cos x dx integrates to:
1/2 * e^-x * (sin x - cos x)

calculating:
limit b->infinity: 1/2 * e^-b * (sin b - cos b) - 1/2 * e^0 * (sin 0 - cos 0)
= 0 - 1 * (0 - 1/2) = 1/2

1/2 matches the book's answer. My question is why does my TI-89 calculator return the wrong answer of 1? I assume the text book devised this problem to exploit some computer weakness?

• Calculus -

Perhaps the calculator is doing a numerical integration and the components are going +-+-+-+- with the phase of the cosine and it is just asking too much of the poor little calculator :)
In other words, I have no idea.

• Calculus -

That's probably close enough Damon. thanks!

## Similar Questions

1. ### Calculus

I'm doing statistics homework and am stuck on a problem using integration. The problem gives a distribution where for x>1, f(x) = k x^-6. I am then asked to "Determine the value of k for which f(x) is a legitimate pdf. " To be a …
2. ### calculus

Assuming that: Definite Integral of e^(-x^2) dx over [0,infinity] = sqrt(pi)/2 Solve for Definite Integral of e^(-ax^2) dx over [-infinity,infinity] I don't know how to approach the new "a" term. I can't use u-substitution, integration …
3. ### Calculus

I need to find the derivative of the following problem via logarithmic differentiation, but I'm getting stuck. I know how to solve via logarithmic differentiation, but I can't figure out how to re-write the exponent(s) as logs. Could …
4. ### calculus

how do you determine the convergence of : definite integral from 1--> infinity of lnx/(x^3)?
5. ### Calculus

Use u = 5x-2 to write an integral equivalent to fnInt((x^2)(5x-2)^(1/2), x, 0, 3) Sorry I had to write it using calculator notation because i can't make a definite integral on my computer.
6. ### calculus

Posted by Paul on Friday, February 19, 2010 at 3:57am. I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}?
7. ### Calculus

Evaluate the definite integral from [0,4] 4x^2 dx, by using its definition as a limit of approximating sums. First, I solve analytically so I know the answer I am trying to reach: 4/3 * x^3 over [0,4] = 4/3 * 4^3 = 256/3 Now, by approximating …
8. ### Calculus

"Leave the answer as a definite integral, but indicate how it could by evaluated by using the fundamental theorem of calculus." I solved the problem to a definite integral. Proceeding via the fundamental theorem, would involve finding …
9. ### calculus

find the definite integral that is equivalent to lim n->infinity of sum over i=(1,n) n/(n^2+i^2) since definite integral of f(x) dx over (a,b) = lim n->infinity sum over i=(1,n) f(a + (b-a)i/n) * (b-a)/n then: f(a + (b-a)i/n) …
10. ### Math (Definite Integrals)

Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2 - x^2) dx -r While I recognize that this looks similar to a circle function, I'm not …

More Similar Questions