Area Under Curve - SHORT TRICK

 Shortcut-Method:

Remember this!
TRICK: Area between two parabolas  and  can be calculated directly by the formula

Explanation:

The given parabola will intersect at points  and

Then the area bounded by given curves is calculated as follows



A = [Area enclosed by  and x -axis] – [Area enclosed by  and x -axis]



Thus, the area between two parabolas can be directly obtained by using the formula derived using integration.

Remember this!

Hence, an area between two parabolas is given as

#Example:

Find the area (in sq. units) under the curves  and

[Options]:

(A)

(B)

(C)

(D)

Answer: (A)

[Solution]:

As the area between the curves  and  is given by



Compare the coefficient of x in equation  with



Now use the formula,



Hence,

Therefore, the correct answer is (A).

Example:

Find the area (in sq. units) under the curve  and

[Options]:

(A)

(B)

(C)

(D)

Answer: (C)

[Solution]:

As the area between the curves  and  is given by

Similarly, the area between the curves  and  is given by



Compare the coefficient of  in equation  with





Now use the formula,



Hence,

Therefore, the correct answer is (C).