The area of the region bounded by the parabol | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The equation of the parabola is $x^{2}=16y$,which gives $x=4\sqrt{y}$ for the first quadrant.The area $A$ is bounded by the curve $x=4\sqrt{y}$,th

Vedclass · Accepted Answer

$\frac{56}{3} 	ext{ sq. units}$

Vedclass · Answer

(B) The equation of the parabola is $x^{2}=16y$,which gives $x=4\sqrt{y}$ for the first quadrant.The area $A$ is bounded by the curve $x=4\sqrt{y}$,the $Y$-axis,and the lines $y=1$ and $y=4$.$A = \int_{1}^{4} x \, dy = \int_{1}^{4} 4\sqrt{y} \, dy$$A = 4 \int_{1}^{4} y^{1/2} \, dy$$A = 4 \left[ \frac{y^{3/2}}{3/2} ight]_{1}^{4}$$A = 4 	imes \frac{2}{3} \left[ y^{3/2} ight]_{1}^{4}$$A = \frac{8}{3} [4^{3/2} - 1^{3/2}]$$A = \frac{8}{3} [8 - 1]$$A = \frac{8}{3} 	imes 7 = \frac{56}{3} 	ext{ sq. units}$

The area of the region bounded by the parabola $x^{2}=16y$,the lines $y=1$,$y=4$,and the $Y$-axis in the first quadrant is:

Similar Questions

The area of the region bounded by the curve $y = \sin 2x$,the $x$-axis,and the lines $x = 0$ and $x = \pi$ is . . . . . . sq. units.

The area of the region bounded by the curve $y=|x-5|$,the $X$-axis,and the lines $x=5$ and $x=6$ is . . . . . . sq. units.

The area (in sq. units) of the region bounded by the curves $y = 2^x$ and $y = |x + 1|$ in the first quadrant is

The area of the bounded region enclosed by the curve $y=3-\left|x-\frac{1}{2}\right|-|x+1|$ and the $x-$axis is

The area of the region bounded by the circle $x^2+y^2=16$ and the lines $x=0$ and $x=4$ in the first quadrant is . . . . . . sq. units. (in $\pi$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module