Advertisements
Advertisements
Question
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
Advertisements
Solution
Let A be the required area
Given equation of the curve y = – 4x
∴ A = A1 + |A2|
= `int_(-1)^0 (-4x) "d"x + |int_0^2 (-4x) "d"x|`
= `-4[x^2/2]_0^1 + |-4[x^2/2]_0^2|`
= `2[0^2 - (-1)^2] + |-2(2^2 - 0^2)|`
= – 2(–1) + |– 2(4)|
= 2 + |– 8|
= 2 + 8
= 10 sq.units
APPEARS IN
RELATED QUESTIONS
Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 = 32.
Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle
`x^2+y^2=4 at (1, sqrt3)`
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 of the smaller part of the circle x2 + y2 = a2 cut off by the line `x = a/sqrt2`
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
Find the area between the curves y = x and y = x2
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`
Find the area of the smaller region bounded by the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1\] and the line \[\frac{x}{3} + \frac{y}{2} = 1 .\]
Find the area of the region.
{(x,y) : 0 ≤ y ≤ x2 , 0 ≤ y ≤ x + 2 ,-1 ≤ x ≤ 3} .
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)`.
Solve the following :
Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.
The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant 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 = `sqrt(9 - x^2)`, X-axis and lines x = 0 and x = 3
Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______
The equation of curve through the point (1, 0), if the slope of the tangent to t e curve at any point (x, y) is `(y - 1)/(x^2 + x)`, is
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.
The area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
If the area enclosed by y = f(x), X-axis, x = a, x = b and y = g(x), X-axis, x = a, x = b are equal, then f(x) = g(x).
The area bounded by the curve `y = 3/2sqrtx`, the line x = 1 and x-axis is ______ sq. units.
