Table of Contents

**What Is The Integral of cos^2x?** this process is the reverse of finding a derivative. Integrations are the anti-derivatives. Integrations are the way of adding the parts to find the whole. Integration is the whole pizza and the slices are the differentiable functions which can be integrated. If f(x) is any function and f′(x) is its derivatives. The integration of f′(x) with respect to dx is given as ∫ f′(x) dx = f(x) + C.

There are two forms of integrals. Indefinite Integrals: It is an integral of a function when there is no limit for integration. It contains an arbitrary constant. Definite Integrals: An integral of a function with limits of integration. There are two values as the limits for the interval of integration. One is the lower limit and the other is the upper limit. It does not contain any constant of integration.

**Integral of cos^2x**

We can’t just integrate cos^2(x) as it is, so we want to change it into another form, which we can easily do using trig identities.

Recall the double angle formula:

** cos(2x) = cos^2(x) – sin^2(x).**

We also know the trig identity

**sin^2(x) + cos^2(x) = 1, **

so combining these we get the equation

**cos(2x) = 2cos^2(x) -1.**

Now we can rearrange this to give:

**cos^2(x) = (1+cos(2x))/2.**

So we have an equation that gives cos^2(x) in a nicer form which we can easily integrate using the reverse chain rule.

This eventually gives us an answer of **x/2 + sin(2x)/4 +c**

**Integral of sin^2x cos^2x**

As sin2x=2sinxcosx

∫sin^2xcos^2xdx=1/4∫(4sin^2xcos^2x)dx

= 1/4∫sin^2(2x)dx

= 1/4∫1−cos4x/2dx

= x/8−18∫cos4xdx

= x/8−18×sin4x/4+c

= x/8−sin4x/32+c

**Integral of 1/cos^2x**

put 1/(cos^2x)=1/(cosx)^2

∫1/(cosx)^2dx

=∫sec2xdx

=tanx+C.

**Integral of cos^2(2x)**

Use the identity:

cos2θ=1+cos2θ/2

so that:

∫cos2(2x)dx

=∫1+cos(4x)/2dx

=1/2∫dx+1/8∫cos(4x)d(4x)

=x/2+1/8sin(4x)+C

**What is the integration of Cos?**

**What is the derivative of cos 2x?**

**Why integration of Sinx is CosX?**

**What is Sinh?**

**What is CSC?**

In a right triangle, the cosecant of an angle is the length of the hypotenuse divided by the length of the opposite side.

**What is the formula for cos2x?**

**How do you find a derivative?**

Find f(x + h).

Plug f(x + h), f(x), and h into the limit definition of a derivative.

Simplify the difference quotient.

Take the limit, as h approaches 0, of the simplified difference quotient.