Question

Let f(x) = x², g(x) = cosx and h(x) = f(g(x)). Area bounded by y = h(x) and x-axis between x = x₁ and x = x₂, where x₁ and x₂ are roots of the equation 18x² - 9πx + π²= 0, is equal to

• A. $\frac { \pi } { 12 }$sq. units
• B. $\frac { \pi } { 6 }$sq. units
• C. $\frac { \pi } { 3 }$sq. units
• D. None of these

Answer 1

Answer: (A)

$\frac { \pi } { 12 }$sq. units

Answer 2

h(x) = cos²x, x, = $\frac { \pi } { 6 }$, x₂ = $\frac { \pi } { 3 }$ Thus required area

$\Delta = \int _ { \pi / 6 } ^ { \pi / 3 } \cos ^ { 2 } x d x = \frac { 1 } { 2 } \left( x + \frac { 1 } { 2 } \sin 2 x \right) _ { \pi / 6 } ^ { \pi / 3 }$

= $\frac { \pi } { 12 }$ sq. units.