Advertisements
Advertisements
प्रश्न
Find the area bounded by the curve y = 2cosx and the x-axis from x = 0 to x = 2π
Advertisements
उत्तर
Given equation of the curve is y = 2 cos x
∴ Area of the shaded region = `int_0^(2pi) 2 cos x "d"x`
= `int_0^(pi/2) 2 cos x "d"x + int_(pi/2)^((3pi)/2) |2 cos x|"d"x + int_((3pi)/2)^(2pi) 2 cos x "d"x`
= `2[sin x]_0^(pi/2) + |[2 sin x]_(pi/2)^((3pi)/2)| + 2[sin x]_((3pi)/2)^(2pi)`
= `2[sin pi/2 - sin 0] + |2(sin (3pi)/2 - sin pi/2)| + 2[sin 2pi - sin (3pi)/2]`
= `2(1) + |2(-1 - 1)| + 2(0 + 1)`
= 2 + 4 + 2
= 8 sq.units
APPEARS IN
संबंधित प्रश्न
Find the area of the sector of a circle bounded by the circle x2 + y2 = 16 and the line y = x in the ftrst quadrant.
Find the area of the region lying in the first quandrant bounded by the curve y2= 4x, X axis and the lines x = 1, x = 4
Draw a rough sketch of the curve and find the area of the region bounded by curve y2 = 8x and the line x =2.
Sketch the graph of y = |x + 4|. Using integration, find the area of the region bounded by the curve y = |x + 4| and x = –6 and x = 0.
Using integration, find the area of the region bounded by the line y − 1 = x, the x − axis and the ordinates x= −2 and x = 3.
Draw a rough sketch of the graph of the function y = 2 \[\sqrt{1 - x^2}\] , x ∈ [0, 1] and evaluate the area enclosed between the curve and the x-axis.
Using integration, find the area of the region bounded by the line 2y = 5x + 7, x-axis and the lines x = 2 and x = 8.
Using definite integrals, find the area of the circle x2 + y2 = a2.
Find the area of the minor segment of the circle \[x^2 + y^2 = a^2\] cut off by the line \[x = \frac{a}{2}\]
Find the area of the region bounded by x2 = 4ay and its latusrectum.
Calculate the area of the region bounded by the parabolas y2 = x and x2 = y.
Draw a rough sketch and find the area of the region bounded by the two parabolas y2 = 4x and x2 = 4y by using methods of integration.
Find the area of the region bounded by the curves y = x − 1 and (y − 1)2 = 4 (x + 1).
Find the area of the region bounded by y = | x − 1 | and y = 1.
Find the area of the region bounded by the curve y = \[\sqrt{1 - x^2}\], line y = x and the positive x-axis.
Find the area enclosed by the curves y = | x − 1 | and y = −| x − 1 | + 1.
Find the area of the region between the parabola x = 4y − y2 and the line x = 2y − 3.
The area bounded by the parabola x = 4 − y2 and y-axis, in square units, is ____________ .
The area of the region formed by x2 + y2 − 6x − 4y + 12 ≤ 0, y ≤ x and x ≤ 5/2 is ______ .
The area bounded by the curves y = sin x between the ordinates x = 0, x = π and the x-axis is _____________ .
The area bounded by the parabola y2 = 4ax, latusrectum and x-axis is ___________ .
The area of the region \[\left\{ \left( x, y \right) : x^2 + y^2 \leq 1 \leq x + y \right\}\] is __________ .
The area bounded by the curve y2 = 8x and x2 = 8y is ___________ .
The area of the circle x2 + y2 = 16 enterior to the parabola y2 = 6x is
Find the coordinates of a point of the parabola y = x2 + 7x + 2 which is closest to the straight line y = 3x − 3.
Sketch the graphs of the curves y2 = x and y2 = 4 – 3x and find the area enclosed between them.
Find the area of the curve y = sin x between 0 and π.
The area of the region bounded by the curve x = y2, y-axis and the line y = 3 and y = 4 is ______.
The area of the region bounded by the curve y = x2 + x, x-axis and the line x = 2 and x = 5 is equal to ______.
Find the area of region bounded by the line x = 2 and the parabola y2 = 8x
Sketch the region `{(x, 0) : y = sqrt(4 - x^2)}` and x-axis. Find the area of the region using integration.
Find the area enclosed by the curve y = –x2 and the straight lilne x + y + 2 = 0
The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 ≤ x ≤ `pi/2` is ______.
The area of the region bounded by the curve x = 2y + 3 and the y lines. y = 1 and y = –1 is ______.
Using integration, find the area of the region in the first quadrant enclosed by the line x + y = 2, the parabola y2 = x and the x-axis.
If a and c are positive real numbers and the ellipse `x^2/(4c^2) + y^2/c^2` = 1 has four distinct points in common with the circle `x^2 + y^2 = 9a^2`, then
The area of the region S = {(x, y): 3x2 ≤ 4y ≤ 6x + 24} is ______.
Using integration, find the area of the region bounded by the curve y2 = 4x and x2 = 4y.
