How to find the antiderivative?

xndx = xn+1+c as long as n does not equal -1. This is essentially the power rule for derivatives in reverse

cf (x)dx = c f (x)dx . That is,a scalar can be pulled out of the integral.

(f (x)+g(x))dx = f (x)dx+g(x)dx .

sin (x)dx = – cos (x)+c cos (x)dx = sin (x)+c sec2(x)dx = tan (x)+c These are the opposite of the trigonometric derivatives.

How to change the Order of integration?

Step 1: Write the limits of integration as inequalities:

N

(0 ≤ y ≤ 1 )

N

(√ y ≤ x ≤ 1 )

Step 2: Find a new set of inequalities that describes the region with the variables in opposite order. Note: This step…

Step 3: Write the new integral with the inequalities from Step 2. Don’t forget to reverse “dx” and “dy”.

Step 4: Integrate as usual. For this double integral, you’ll…

How do you calculate an integral?

1) Set up integral notation, placing the smaller number at the bottom and the larger number at the top: 2) Find the integral, using the usual rules of integration. 3) Substitute the top number for x and then solve: 4) Add a subtraction sign and then substitute the bottom number for x, solving the integral:

What is complex line integral?

In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour integral as well, although that is typically reserved for line integrals in the complex plane.

What is the integral of sin x squared?

Integration of Sin Squared x. In this tutorial we shall derive the integral of sine squared x. The integration is of the form. I = ∫ sin 2 x d x. This integral cannot be evaluated by the direct formula of integration, so using the trigonometric identity of half angle sin 2 x = 1 – cos. ⁡. 2 x 2, we have. I = ∫ ( 1 – cos.

What is the integral of Cos?

The integral of cos(2x) is 1/2 x sin(2x) + C, where C is equal to a constant. The integral of the function cos(2x) can be determined by using the integration technique known as substitution. In calculus, substitution is derived from the chain rule for differentiation.