
What is the integral of
Answer
452.7k+ views
Hint: We will use the trigonometric identities to find the integral. First, we will change the given trigonometric function to an equivalent simple form. And then, we will integrate the function with respect to We will use the identity
Complete step by step solution:
Let us consider the given trigonometric function
We are asked to find the integral of the given function with respect to
That is, we need to find the value of
We know the trigonometric identity given by
In this identity, we will put instead of since our function contains
We will get
We can write this as
Now, we can change the integral using the above equation.
We will get
Let us take out of the integral sign, since it is a constant term. We know that we can take the constant term if it is multiplied with a variable term. If the operation is addition, then we cannot take the term out.
Now, we will get
Now, we can use the linearity property of integration.
We will get
Let us consider the first integral,
We know that the integral of the Cosine function is the Sine function.
So, from the second integral, we will get
So, the integral will become
Hence the integral of the given function is
Note: Remember the similar trigonometric identity By applying this identity, we can find the integral of in the exact way we have found the integral of The linearity property of integration is where are constants and are functions of
Complete step by step solution:
Let us consider the given trigonometric function
We are asked to find the integral of the given function with respect to
That is, we need to find the value of
We know the trigonometric identity given by
In this identity, we will put
We will get
We can write this as
Now, we can change the integral using the above equation.
We will get
Let us take
Now, we will get
Now, we can use the linearity property of integration.
We will get
Let us consider the first integral,
We know that the integral of the Cosine function is the Sine function.
So, from the second integral, we will get
So, the integral will become
Hence the integral of the given function is
Note: Remember the similar trigonometric identity
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