Advertisements
Advertisements
प्रश्न
Fill in the blank :
The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 is _______.
Advertisements
उत्तर
Required area = `int_3^9 y*dx`
= `int_3^9 x^2*dx`
= `[x^3/3]_3^9`
= `(1)/(3)(9^3 - 3^3)`
= `(1)/(3)(729 - 27)`
= `(702)/(3)`
= 234 sq. units.
APPEARS IN
संबंधित प्रश्न
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 of the smaller part of the circle x2 + y2 = a2 cut off by the line `x = a/sqrt2`
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(16 - x^2)`, x = 0, x = 4
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4
Find the area of the region bounded by the parabola y2 = 4x and the line x = 3.
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
State whether the following is True or False :
The area bounded by the curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.
Choose the correct alternative:
Area of the region bounded by the curve y = x3, x = 1, x = 4 and the X-axis is ______
Choose the correct alternative:
Using the definite integration area of the circle x2 + y2 = 16 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 ______
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
Find the area of the circle x2 + y2 = 62
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 ______
`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
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
Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
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.
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?
What is the area enclosed by the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?
