0 pi sin 6xcos 5xdx is equal to 594021949

$$\int_0^\pi {{{\sin }^6}x.{{\cos }^5}x\,dx} $$ is equal to :

A. $$2\int_0^{\frac{\pi }{2}} {{{\sin }^{50}}x.{{\cos }^{47}}x\,dx} $$

B. $$0$$

C. $$1$$

D. none of these

Answer : $$0$$

Solution :
$$\eqalign{ & I = \int_0^\pi {{{\sin }^6}x.{{\cos }^5}x\,dx} = \int_0^\pi {{{\sin }^6}\left( {\pi - x} \right).{{\cos }^5}\left( {\pi - x} \right)\,dx} = - I \cr & \therefore I = 0 \cr} $$

Releted MCQ Question on
Calculus >> Application of Integration

Releted Question 1

The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-

A. $$\left( {x - 1} \right)\cos \left( {3x + 4} \right)$$

B. $$\sin \,\left( {3x + 4} \right)$$

C. $$\sin \,\left( {3x + 4} \right) + 3\left( {x - 1} \right)\cos \left( {3x + 4} \right)$$

D. none of these

View Answer

Releted Question 2

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is-

A. $$1$$

B. $$2$$

C. $$2\sqrt 2 $$

D. $$4$$

View Answer

Releted Question 3

The area bounded by the curves $$y = \sqrt x ,\,2y + 3 = x$$ and $$x$$-axis in the 1^st quadrant is-

A. $$9$$

B. $$\frac{{27}}{4}$$

C. $$36$$

D. $$18$$

View Answer

Releted Question 4

The area enclosed between the curves $$y = a{x^2}$$ and $$x = a{y^2}\left( {a > 0} \right)$$ is 1 sq. unit, then the value of $$a$$ is-

A. $$\frac{1}{{\sqrt 3 }}$$

B. $$\frac{1}{2}$$

C. $$1$$

D. $$\frac{1}{3}$$

View Answer

$$\int_0^\pi {{{\sin }^6}x.{{\cos }^5}x\,dx} $$ is equal to :

Releted MCQ Question on
Calculus >> Application of Integration

The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is-

The area bounded by the curves $$y = \sqrt x ,\,2y + 3 = x$$ and $$x$$-axis in the 1^st quadrant is-

The area enclosed between the curves $$y = a{x^2}$$ and $$x = a{y^2}\left( {a > 0} \right)$$ is 1 sq. unit, then the value of $$a$$ is-

Practice More Releted MCQ Question on
Application of Integration

Practice More MCQ Question on Maths Section

$$\int_0^\pi {{{\sin }^6}x.{{\cos }^5}x\,dx} $$ is equal to :

Releted MCQ Question on Calculus >> Application of Integration

The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is-

The area bounded by the curves $$y = \sqrt x ,\,2y + 3 = x$$ and $$x$$-axis in the 1st quadrant is-

The area enclosed between the curves $$y = a{x^2}$$ and $$x = a{y^2}\left( {a > 0} \right)$$ is 1 sq. unit, then the value of $$a$$ is-

Practice More Releted MCQ Question on Application of Integration

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Releted MCQ Question on
Calculus >> Application of Integration

The area bounded by the curves $$y = \sqrt x ,\,2y + 3 = x$$ and $$x$$-axis in the 1^st quadrant is-

Practice More Releted MCQ Question on
Application of Integration