Advertisements
Advertisements
प्रश्न
Find the area under the given curve and given line:
y = x2, x = 1, x = 2 and x-axis
Advertisements
उत्तर
The vertex of the parabola y = x2 is (0, 0). The line OY is symmetric.
Area of the region bounded by y = x2, x = 1, x = 2 and x-axis
= Area of the region PLMQ
`int_1^2 y dx = int_1^2 x^2 dx`
`= [x^3/3]_0^2`
`= 8/3 - 1/3`
`= 7/3` square unit
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Find the area of the region bounded by x2 = 4y, y = 2, y = 4 and the y-axis in the first quadrant.
Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`
Find the area of the region bounded by the parabola y = x2 and y = |x| .
Find the area bounded by the curve x2 = 4y and the line x = 4y – 2
Find the area of the smaller region bounded by the ellipse `x^2/a^2 + y^2/b^2 = 1` and the line `x/a + y/b = 1`
Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).
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).
Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
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 bounded by the following curve, the X-axis and the given line:
y = 2 – x2, x = –1, x = 1
Choose the correct alternative :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
Using definite integration, area of the circle x2 + y2 = 49 is _______.
State whether the following is True or False :
The area bounded by the curve x = g (y), Y-axis and bounded between the lines y = c and y = d is given by `int_"c"^"d"x*dy = int_(y = "c")^(y = "d") "g"(y)*dy`
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|`.
If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.
Choose the correct alternative:
Using the definite integration area of the circle x2 + y2 = 16 is ______
The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x) "d"x`
The area of the region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 4 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 the area of the region bounded by the curve y = `sqrt(2x + 3)`, the X axis and the lines x = 0 and x = 2
Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant
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 region bounded by the curve y = `sqrt(36 - x^2)`, the X-axis lying in the first quadrant and the lines x = 0 and x = 6
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
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 ______.
Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.
Which integral gives the area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\]?
