Advertisements
Advertisements
प्रश्न
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
Advertisements
उत्तर
The area enclosed between the parabola, 4y = 3x2, and the line, 2y = 3x + 12, is represented by the shaded area OBAO as

The points of intersection of the given curves are A (–2, 3) and (4, 12).
We draw AC and BD perpendicular to x-axis.
∴ Area OBAO = Area CDBA – (Area ODBO + Area OACO)

APPEARS IN
संबंधित प्रश्न
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 region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.
Find the area of the region bounded by the ellipse `x^2/4 + y^2/9 = 1.`
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
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0, y = 1 and y = 4
Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`
Find the area enclosed between the parabola y2 = 4ax and the line y = mx
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).
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 x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant 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`
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.
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Area of the region bounded by the curve x = y2, the positive Y axis and the lines y = 1 and y = 3 is ______
State whether the following statement is True or False:
The equation of the area of the circle is `x^2/"a"^2 + y^2/"b"^2` = 1
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`
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
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 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 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
The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 is ______
The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 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:
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 included between the parabolas y2 = 4a(x +a) and y2 = 4b(x – a), b > a > 0, is
The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`
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 ______.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
The area bounded by the curve, y = –x, X-axis, x = 1 and x = 4 is ______.
The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.
Which expression gives physical area when the curve \[y=f(x)\] lies below the \[x\]-axis from \[x=a\] to \[x=b\]?
Why cannot a curve crossing the \[x\]-axis within \[a,b\] be integrated directly from \[a\] to \[b\] to obtain total area?
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?
Why is the area enclosed by \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] written as \[4\int_0^a y\,dx\]?
