If the area bounded by y = x , y = s i n x and x = π 2 is π 2 k - 1 sq. units, then the value of k is equal to

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Question: Answered & Verified by Expert

If the area bounded by

y = x, y = s i n x

and

x = \frac{π}{2}

is

(\frac{π^{2}}{k} - 1)

sq. units, then the value of

k

is equal to

MathematicsArea Under CurvesJEE Main

Options:

A $2$
B $4$
C $6$
D $8$

Solution:

2772 Upvotes Verified Answer

The correct answer is:

8

Required area

= ar (Δ A O B) - \int_{0}^{\frac{π}{2}} \sin x d x

= \underset{\frac{1}{2} \cdot b a s e \cdot h e i g h t}{\underset{⏟}{\frac{1}{2} \cdot \frac{π}{2} \cdot \frac{π}{2}}} - 1

= \frac{π^{2}}{8} - 1

sq. units

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