Advertisements
Advertisements
प्रश्न
The area of the region bounded by the curve y = x + 1 and the lines x = 2 and x = 3 is ______.
पर्याय
`7/2` sq.units
`9/2` sq.units
`11/2` sq.units
`13/2` sq.units
Advertisements
उत्तर
The area of the region bounded by the curve y = x + 1 and the lines x = 2 and x = 3 is `7/2` sq.units.
Explanation:
Given equation of lines are = x + 1, x = 2 and x = 3
Required area = `int_2^3 (x + 1) "d"x`
= `[x^2/2 + x]_2^3`
= `(9/2 + 3) - (4/2 + 2)`
= `15/2 - 4`
= `7/2` sq.units
APPEARS IN
संबंधित प्रश्न
Find the area bounded by the curve y2 = 4ax, x-axis and the lines x = 0 and x = a.
Using integration, find the area of the region bounded by the lines y = 2 + x, y = 2 – x and x = 2.
Using the method of integration find the area of the region bounded by lines: 2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0
Find the area of the region lying in the first quandrant bounded by the curve y2= 4x, X axis and the lines x = 1, x = 4
Find the area lying above the x-axis and under the parabola y = 4x − x2.
Find the area under the curve y = \[\sqrt{6x + 4}\] above x-axis from x = 0 to x = 2. Draw a sketch of curve also.
Draw a rough sketch of the graph of the function y = 2 \[\sqrt{1 - x^2}\] , x ∈ [0, 1] and evaluate the area enclosed between the curve and the x-axis.
Determine the area under the curve y = `sqrt(a^2-x^2)` included between the lines x = 0 and x = a.
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 region {(x, y) : y2 ≤ 3x, 3x2 + 3y2 ≤ 16} and find the area enclosed by the region using method of integration.
Find the area of the region bounded by \[y = \sqrt{x}\] and y = x.
Find the area of the circle x2 + y2 = 16 which is exterior to the parabola y2 = 6x.
Find the area bounded by the lines y = 4x + 5, y = 5 − x and 4y = x + 5.
The area bounded by the parabola x = 4 − y2 and y-axis, in square units, is ____________ .
The area bounded by the curves y = sin x between the ordinates x = 0, x = π and the x-axis is _____________ .
The area of the region \[\left\{ \left( x, y \right) : x^2 + y^2 \leq 1 \leq x + y \right\}\] is __________ .
The area of the region (in square units) bounded by the curve x2 = 4y, line x = 2 and x-axis is
The area bounded by the curve y2 = 8x and x2 = 8y is ___________ .
The area of the circle x2 + y2 = 16 enterior to the parabola y2 = 6x is
Area lying in first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2, is
Using the method of integration, find the area of the triangle ABC, coordinates of whose vertices area A(1, 2), B (2, 0) and C (4, 3).
Find the equation of the standard ellipse, taking its axes as the coordinate axes, whose minor axis is equal to the distance between the foci and whose length of the latus rectum is 10. Also, find its eccentricity.
Find the area of the region bound by the curves y = 6x – x2 and y = x2 – 2x
Using integration, find the area of the region bounded by the parabola y2 = 4x and the circle 4x2 + 4y2 = 9.
The area enclosed by the circle x2 + y2 = 2 is equal to ______.
The area of the region bounded by the curve y = x2 + x, x-axis and the line x = 2 and x = 5 is equal to ______.
Find the area of the region bounded by the curves y2 = 9x, y = 3x
Using integration, find the area of the region bounded by the line 2y = 5x + 7, x- axis and the lines x = 2 and x = 8.
Find the area bounded by the curve y = sinx between x = 0 and x = 2π.
Draw a rough sketch of the region {(x, y) : y2 ≤ 6ax and x 2 + y2 ≤ 16a2}. Also find the area of the region sketched using method of integration.
The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 ≤ x ≤ `pi/2` is ______.
The area of the region bounded by the ellipse `x^2/25 + y^2/16` = 1 is ______.
The curve x = t2 + t + 1,y = t2 – t + 1 represents
Area of the region bounded by the curve `y^2 = 4x`, `y`-axis and the line `y` = 3 is:
What is the area of the region bounded by the curve `y^2 = 4x` and the line `x` = 3.
The area bounded by the curve `y = x^3`, the `x`-axis and ordinates `x` = – 2 and `x` = 1
Find the area bounded by the curve y = |x – 1| and y = 1, using integration.
Let a and b respectively be the points of local maximum and local minimum of the function f(x) = 2x3 – 3x2 – 12x. If A is the total area of the region bounded by y = f(x), the x-axis and the lines x = a and x = b, then 4A is equal to ______.
Sketch the region enclosed bounded by the curve, y = x |x| and the ordinates x = −1 and x = 1.
