
If then
A.
B.
C.
D.None of these
Answer
505.8k+ views
Hint: We consider the left-hand side of the expression and try to solve it by integrating step by step. In order to achieve the final expression, we need to do some adjustment operations in the expression. Once the final form of the expression is obtained, we can easily determine the required values of a and b.
Formula Used:
In order to solve this expression some important formulas are used that is,
Where, is the constant of integration.
Complete step by step solution
Given:
The expression .
Now, we will be solving the left hand side of the above expression, we have,
On rearranging the term by multiplying and dividing it with we get,
Where, we know that and .
Now, we know that the term can be written as the formula,
We know that the values for both and are negative in the third quadrant so, we get,
So, the value of a will be equal to,
Then finally, the integral reduces to,
Also, the above expression can also be written as:
Where, and are arbitrary constants, whose values are and (b belongs to real number).
The correct option is (B) that is .
Note: We have to reduce the expression in simplest form as given in the question that is why we had to do some rearrangements in the expression by multiplying-dividing with a number and using trigonometric relations.
Formula Used:
In order to solve this expression some important formulas are used that is,
Where,
Complete step by step solution
Given:
The expression
Now, we will be solving the left hand side of the above expression, we have,
On rearranging the term by multiplying and dividing it with
Where, we know that
Now, we know that the term
We know that the values for both
So, the value of a will be equal to,
Then finally, the integral reduces to,
Also, the above expression can also be written as:
Where,
The correct option is (B) that is
Note: We have to reduce the expression in simplest form as given in the question that is why we had to do some rearrangements in the expression by multiplying-dividing with a number and using trigonometric relations.
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