Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the following curve, the X-axis and the given line:
y = 2 – x2, x = –1, x = 1
Advertisements
उत्तर
Let A be the required area.
Consider the equation y = 2 – x2.
∴ A = `int_(-1)^(1) y*dx`
= `int_(-1)^(1)(2 - x^2)*dx`
= `[2x - x^3/3]_(-1)^(1)`
= `[2 xx 1 - 1^3/3] - [2 xx (-1) - (-1)^3/3]`
= `(2 - 1/3) - (-2 + 1/3)`
= `(5)/(3) - ((-5)/3)`
∴ A = `(10)/(3)` sq. units.
APPEARS IN
संबंधित प्रश्न
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
Find the area under the given curve and given line:
y = x2, x = 1, x = 2 and x-axis
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices are A (4 , 1), B (6, 6) and C (8, 4).
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9 "at" (-1,2sqrt2)`.
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
Choose the correct alternative:
Using the definite integration area of the circle x2 + y2 = 16 is ______
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
Find the area of the region bounded by the curve y = (x2 + 2)2, the X-axis and the lines x = 1 and x = 3
Find the area of the circle x2 + y2 = 16
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 is ______
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
If a2 + b2 + c2 = – 2 and f(x) = `|(1 + a^2x, (1 + b^2)x, (1 + c^2)x),((1 + a^2)x, 1 + b^2x, (1 + c^2)x),((1 + a^2)x, (1 + b^2)x, 1 + c^2x)|` then f(x) is a polynomial of degree
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
The area of the region bounded by the curve y = x2, x = 0, x = 3, and the X-axis is ______.
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.
For an area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\], which strips are used?
A curve crosses the \[x\]-axis, forming area \[A_1\] below the axis and area \[A_2\] above the axis. What is its total area?
What is the area enclosed by the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
