Question

∫[e^(3t)sin(3t),dt]= ;limit(0,π)

Answer 1

you will definitely need to use integration by parts

Answer 2

if you know the product rule, you can derive the formula for integration by parts

Answer 3

if you don't know the product rule, you can use the definition of derivative to find the formual for the product rule

Answer 4

Integrate by parts, setting e^(3x) equal to u and the trig function equal to v' each time. The 3's will cancel out every time, and you'll end up in the third term with the original integral; add it to the left and divide by two, you'll end up getting\[e^{3t}*1/6*(\sin(3t)-\cos(3t)).\] Evaluate it at the limits and out pops the value. :P

Answer 5

that is the exact ans I got when I integrated it, QuantumModulus.....But my final ans was -1/6(1+e^3pi)

Answer 6

Thenk you!