Jeann25 said:That was very helpful, thank you. Could I also get help with this one pls? :) I just seem to have a hard time figuring out where to start on these.
The integral of (sin(ln x))/x dx
The formula for the integral of (sin(x))^1/2)(cos^3(x)) dx is ∫ (sin(x))^1/2 (cos^3(x)) dx = -2/5 (cos^2(x))^3/2 + C.
To solve the integral of (sin(x))^1/2)(cos^3(x)) dx, you can use the substitution method by setting u = sin(x) and du = cos(x) dx. You can also use the trigonometric identity sin^2(x) + cos^2(x) = 1 to simplify the integral.
The domain of the integral of (sin(x))^1/2)(cos^3(x)) dx is all real numbers.
Yes, you can also use integration by parts to solve the integral of (sin(x))^1/2)(cos^3(x)) dx. Set u = (sin(x))^1/2 and dv = cos^3(x) dx, and then use the formula ∫ u dv = u v - ∫ v du.
The integral of (sin(x))^1/2)(cos^3(x)) dx has applications in physics, engineering, and other fields that involve calculating areas under curves or finding the average value of a function over a specific interval. It can also be used to solve differential equations and in finding antiderivatives of more complex trigonometric functions.