Advertisements
Advertisements
प्रश्न
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y = 5x + 7, x = 2, x = 8
Advertisements
उत्तर
Let A be the required area.
Consider the equation 2y = 5x + 7
i.e. y = `(5x + 7)/(2)`
∴ A = `int_2^8 y*dx`
= `int_2^8 (5x + 7)/(2)*dx`
= `(1)/(2) int_2^8 (5x + 7)*dx`
= `(1)/(2)[(5x^2)/(2) + 7x]_2^8`
= `(1)/(2)[((5 xx 8^2)/2 + 7 xx 8) - ((5 xx 2^2)/2 + 7 xx 2)]`
= `(1)/(2)[(160 + 56) - (10 + 14)]`
= `(1)/(2)(216 - 24)`
= `(1)/(2) xx 192`
∴ A = 96 sq. units.
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by y2 = 9x, x = 2, x = 4 and the x-axis in the first quadrant.
Find the area of the region bounded by the ellipse `x^2/16 + y^2/9 = 1.`
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 between the curves y = x and y = x2
Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
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).
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
Fill in the blank :
Area of the region bounded by x2 = 16y, y = 1, y = 4 and the Y-axis, lying in the first quadrant is _______.
Choose the correct alternative:
Area of the region bounded by y2 = 16x, x = 1 and x = 4 and the X axis, lying in the first quadrant is ______
Choose the correct alternative:
Area of the region bounded by x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 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 the area of the region bounded by the curve x = `sqrt(25 - y^2)`, the Y-axis lying in the first quadrant and the lines y = 0 and y = 5
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 = ?
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
The area bounded by the X-axis, the curve y = f(x) and the lines x = 1, x = b is equal to `sqrt("b"^2 + 1) - sqrt(2)` for all b > 1, then f(x) 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 area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`
The area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
For an area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\], which strips are used?
Which integral gives the area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\]?
For the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\], which expression for \[y\] is obtained before selecting the first-quadrant branch?
Which integral represents the enclosed area of the ellipse after using the positive first-quadrant value of \[y\]?
Which antiderivative is used in evaluating \[\int \sqrt{a^2-x^2}\,dx\] for the ellipse area?
