a Find a function Fx such that Fx e3xsin5x and F010Solution

Solution

(a) Find a function F(x) such that F\'(x) = e^3x*sin(5x) and F(0)=10 we know that the integral of the derivative gives the actual function. so, we need to find the integral of the given derivative of the function we will get F(x) = (1/34)e^(3x)(3sin(5x) - 5cos(5x)) + c now, replace the value of x = 0 And see if we will get the value 10. F(0) = -5/34 + c replace the value of F(0) = 10 10 = -5/34 + c c = 10 + 5/34 c = 345/34 so the required function is F(x) = (1/34)e^(3x)(3sin(5x) - 5cos(5x)) + 345/34 Hope this will help you!