Advertisements
Advertisements
Question
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
Advertisements
Solution
Let A be the required area.
Given equation of the curve is y = `sqrt(2x + 3)`
∴ A = `int_0^2 y "d"x`
= `int_0^2 sqrt(2x + 3) "d"x`
= `int_0^2 (2x + 3)^(1/2) "d"x`
= `[((2x + 3)^(3/2))/(3/2) xx 1/2]_0^2`
= `1/3[(2x + 3)^(3/2)]_0^2`
= `1/3[(4 + 3)^(5/2) - (0 + 3)^(3/2)]`
= `1/3[(7)^(3/2) - (3)^(3/2)]`
∴ A = `1/3(7sqrt(7) - 3sqrt(3))` sq.units
APPEARS IN
RELATED QUESTIONS
Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle
`x^2+y^2=4 at (1, sqrt3)`
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
Find the area under the given curve and given line:
y = x2, x = 1, x = 2 and x-axis
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
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 of the region bounded by the parabola y2 = 16x and the line x = 4.
Using definite integration, area of the circle x2 + y2 = 49 is _______.
State whether the following is True or False :
The area of the portion lying above the X-axis is positive.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
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 ______
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 circle x2 + y2 = 16 is ______
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
`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______
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 ______.
The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 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 figure shows as triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x2 is equal to ______.
The area (in sq. units) of the region {(x, y) : y2 ≥ 2x and x2 + y2 ≤ 4x, x ≥ 0, y ≥ 0} is ______.
Find the area of the regions bounded by the line y = −2x, the X-axis and the lines x = −1 and x = 2.
Why cannot a curve crossing the \[x\]-axis within \[a,b\] be integrated directly from \[a\] to \[b\] to obtain total area?
A curve crosses the \[x\]-axis, forming area \[A_1\] below the axis and area \[A_2\] above the axis. What is its total area?
Why is the area enclosed by \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] written as \[4\int_0^a y\,dx\]?
