Solving the Integral of sin(u) using Integration by Substitution

∫sin u du

To solve the integral of sin(u) du, we can use the integration by substitution technique

To solve the integral of sin(u) du, we can use the integration by substitution technique. Let’s first define a new variable, let’s say v, which is equal to u. So v = u. Then, we can find the derivative of v with respect to u to be dv/du = 1.

Now, we need to rewrite the integral in terms of the new variable v. Since v = u, we can substitute u in the integral with v. So the integral becomes:

∫sin(u) du = ∫sin(v) dv.

Now, we can solve this integral in terms of v. The integral of sin(v) dv is equal to -cos(v) + C, where C is the constant of integration. Therefore, the final solution to the integral is:

∫sin(u) du = -cos(v) + C.

However, we initially defined v = u, so we can substitute v back into the solution:

∫sin(u) du = -cos(v) + C = -cos(u) + C.

So the final answer to the integral is -cos(u) + C, where C represents the constant of integration.

More Answers: