Advertisements
Advertisements
प्रश्न
The area of the region bounded by the curve y = x2 and the line y = 16 ______.
पर्याय
`32/3`
`256/3`
`64/3`
`128/3`
उत्तर
The area of the region bounded by the curve y = x2 and the line y = 16 `256/3`.
Explanation:
Since area = `2 int_0^16 sqrt(y) "d"y`
APPEARS IN
संबंधित प्रश्न
Prove that the curves y2 = 4x and x2 = 4y divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.
Area bounded by the curve y = x3, the x-axis and the ordinates x = –2 and x = 1 is ______.
Find the equation of a curve passing through the point (0, 2), given that the sum of the coordinates of any point on the curve exceeds the slope of the tangent to the curve at that point by 5
Sketch the graph y = | x + 3 |. Evaluate \[\int\limits_{- 6}^0 \left| x + 3 \right| dx\]. What does this integral represent on the graph?
Draw a rough sketch of the curve \[y = \frac{x}{\pi} + 2 \sin^2 x\] and find the area between the x-axis, the curve and the ordinates x = 0 and x = π.
Find the area bounded by the curve y = 4 − x2 and the lines y = 0, y = 3.
Using integration, find the area of the region bounded by the triangle ABC whose vertices A, B, C are (−1, 1), (0, 5) and (3, 2) respectively.
Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4).
Find the area of the circle x2 + y2 = 16 which is exterior to the parabola y2 = 6x.
Make a sketch of the region {(x, y) : 0 ≤ y ≤ x2 + 3; 0 ≤ y ≤ 2x + 3; 0 ≤ x ≤ 3} and find its area using integration.
Find the area of the region between the parabola x = 4y − y2 and the line x = 2y − 3.
The area bounded by the curve y = loge x and x-axis and the straight line x = e is ___________ .
The area bounded by the curves y = sin x between the ordinates x = 0, x = π and the x-axis is _____________ .
The ratio of the areas between the curves y = cos x and y = cos 2x and x-axis from x = 0 to x = π/3 is ________ .
The area bounded by the curve y = 4x − x2 and the x-axis is __________ .
Area bounded by the curve y = x3, the x-axis and the ordinates x = −2 and x = 1 is ______.
Sketch the graphs of the curves y2 = x and y2 = 4 – 3x and find the area enclosed between them.
Using integration, find the area of the smaller region bounded by the ellipse `"x"^2/9+"y"^2/4=1`and the line `"x"/3+"y"/2=1.`
The area of the region bounded by the curve x = y2, y-axis and the line y = 3 and y = 4 is ______.
Find the area of the region bounded by the curves y2 = 9x, y = 3x
Find the area bounded by the curve y = sinx between x = 0 and x = 2π.
The area of the region bounded by the circle x2 + y2 = 1 is ______.
The area of the region enclosed by the parabola x2 = y, the line y = x + 2 and the x-axis, is
Let the curve y = y(x) be the solution of the differential equation, `("dy")/("d"x) = 2(x + 1)`. If the numerical value of area bounded by the curve y = y(x) and x-axis is `(4sqrt(8))/3`, then the value of y(1) is equal to ______.
Make a rough sketch of the region {(x, y) : 0 ≤ y ≤ x2 + 1, 0 ≤ y ≤ x + 1, 0 ≤ x ≤ 2} and find the area of the region, using the method of integration.
Find the area of the region bounded by the curve x2 = 4y and the line x = 4y – 2.
