calculus
posted by Bryant
Let z = ∫(e^sin(t)dt) from x to y
a = x
b = y
I tried thinking about it like a chain rule but even then i'm a little unsure.
I know dz/dt = e^sin(t). Can you please point me in the right direction if i'm supposed to use the chain rule.

MathMate
Don't know if you really meant
∫sin(t)e^t dt
If that's the case, try differentiate using the chain rule,
sin(t)e^t
and
cos(t)e^t
You should be able to figure out the integral from the results.
The original integral you posted does not seem to have an analytic solution. A series solution is (almost always) available but does not fit your bill. 
Anonymous
uh no i meant what i typed which is e^(sin(t))

Steve
In that case, I fear there is no solution using elementary functions.
who posed such a problem? It's solvable numerically, using a Taylor series, but not symbolically.
Respond to this Question
Similar Questions

Math integrals
What is the indefinite integral of ∫ [sin (π/x)]/ x^2] dx ? 
calculus
Let z = ∫e^(sin(t))dt from x to y a = x b = y I tried thinking about it like a chain rule but even then i'm a little unsure. I know dz/dt = e^(sin(t)). Can you please point me in the right direction if i'm supposed to use the … 
calculus
Let z = ∫e^(sin(t))dt from x to y a = x b = y I tried thinking about it like a chain rule but even then i'm a little unsure. I know dz/dt = e^(sin(t)). Can you please point me in the right direction if i'm supposed to use the … 
calculus
Find dz/dy and dz/dx Let z = ∫e^(sin(t))dt from x to y a = x b = y I tried thinking about it like a chain rule but even then i'm a little unsure. I know dz/dt = e^(sin(t)). Can you please point me in the right direction if i'm … 
Calculus
Hello, I just wanted to verify if my work was good. Calculate the following integral by parts: ∫ upper limit is 1/5 and lower limit is 1/10. of 10sin^1 (5x)dx so first I named the variables: u = 10 sin^1 (5x) du = 50 / sqr(125x^2) … 
calculus II
∫ tan^2 x sec^3 x dx If the power of the secant n is odd, and the power of the tangent m is even, then the tangent is expressed as the secant using the identity 1 + tan^2 x = sec^2 x I thought that since tan is even and sec is … 
Calculus
Use a Riemann sum with n = 3 terms and the right endpoint rule to approx. ∫(1, 2) sin(1/x)dx. My teacher just needs the terms written out, no need to add or multiply. This is a problem she did up on the board, so here's her answer: … 
Calculus
Alright, I want to see if I understand the language of these two problems and their solutions. It asks: If F(x) = [given integrand], find the derivative F'(x). So is F(x) just our function, and F'(x) our antiderivative? 
Calculus
Evaluate ∫ (cos(x))^(1/2)sin(x)dx Let u = cos(x)? 
Calculus
Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help. Calculus  Steve, Tuesday, January 12, 2016 at 12:45am …