what is the anti derivative of 2sinxdx?

Question

Calculus integrals

Answer 1

-2cosx + c

Answer 2

Your first step in solving this is to recognize your higher derivatives. For example

y = sin(x)
y' = cos(x)
y'' = -sin(x)
y''' = -cos(x)
y'''' = -(-sin(x)) = sin(x)

Note how it repeats. Also, note that each term in the middle is sandwiched by the positive version of what it's not on the top, and the negative version on the bottom. For example, cosx is sandwiched by sinx on the top and -sinx on the bottom.

This is what we keep in mind when solving this antiderivative (or integral).

So we want to solve Integral (2sinx dx)
First, we pull out all constants; in this case, it's a 2. We bring it to the outside of the Integral.

2 * Integral (sinx dx)

Now, we take the antiderivative. What's the antiderivative of sin(x)? Let's ask ourselves first what the derivative of sin(x) is; it's cos(x). Therefore, the integral must be the opposite sign of the derivative, so it's -cos(x). Remember to always add constants when finding general antiderivatives, so we have to add a C.

2 * (-cos(x)) + C
-2cos(x) + C

Answer 3

It's -2*cos x + C.

Answer 4

-2 cos x + C

Answer 5

integral 2sinxdx
2 int sinxdx
2 (-cosx)
-2cosx + c where c is a constant

Answer 6

-2cosx+C

Answer 7

-2Cos(x)