If the area bounded by y=x,y=sinx and x=(π /2) is (((π )2/k) - 1) sq. units, then the value of k is equal to

Question

If the area bounded by y=x,y=sinx and x=(π /2) is (((π )2/k) - 1) sq. units, then the value of k is equal to (A) 2 (B) 4 (C) 6 (D) 8

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-m1ysbcdytlfr.png" /> Required area =ar(Δ A O B)- displaystyle ∫ 0(π /2)sin xdx = underset(1/2) ⋅ b a s e ⋅ h e i g h t underbrace(1/2) ⋅ (π /2) ⋅ (π /2)-1 =(π 2/8)-1 sq. units

Q. If the area bounded by $y = x, y = s in x$ and $x = \frac{π}{2}$ is $(\frac{( π ) ^{2}}{k} - 1)$ sq. units, then the value of $k$ is equal to

$2$

$4$

$6$

$8$

Required area $= a r (Δ A OB) - \int_{0}^{\frac{π}{2}} s in x d x$
$= \frac{1}{2} \cdot ba se \cdot h e i g h t \frac{1}{2} \cdot \frac{π}{2} \cdot \frac{π}{2} - 1$
$= \frac{π ^{2}}{8} - 1$ sq. units

Q. If the area bounded by y=x,y=sinx and x=2π​ is (k(π)2​−1) sq. units, then the value of k is equal to

2

4

6

8

Required area =ar(ΔAOB)−∫02π​​sinxdx =21​⋅base⋅height21​⋅2π​⋅2π​​​−1 =8π2​−1 sq. units

Q. If the area bounded by $y = x, y = s in x$ and $x = \frac{π}{2}$ is $(\frac{( π ) ^{2}}{k} - 1)$ sq. units, then the value of $k$ is equal to

$2$

$4$

$6$

$8$

Required area $= a r (Δ A OB) - \int_{0}^{\frac{π}{2}} s in x d x$
$= \frac{1}{2} \cdot ba se \cdot h e i g h t \frac{1}{2} \cdot \frac{π}{2} \cdot \frac{π}{2} - 1$
$= \frac{π ^{2}}{8} - 1$ sq. units