Advertisements
Advertisements
प्रश्न
Find the area of the curve y = sin x between 0 and π.
Advertisements
उत्तर
We have
Area OAB = `int_0^pi t"d"x`
= `int_0^pi sinx "d"x`
= `|-cos x|_0^x`
= cos0 – cosπ
= 2 sq.units
APPEARS IN
संबंधित प्रश्न
Using integration, find the area of the region bounded by the lines y = 2 + x, y = 2 – x and x = 2.
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
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.
Sketch the graph y = |x + 1|. Evaluate\[\int\limits_{- 4}^2 \left| x + 1 \right| dx\]. What does the value of this integral represent on the graph?
Compare the areas under the curves y = cos2 x and y = sin2 x between x = 0 and x = π.
Find the area of the region bounded by the curve \[x = a t^2 , y = 2\text{ at }\]between the ordinates corresponding t = 1 and t = 2.
Find the area of the region bounded by the curve \[a y^2 = x^3\], the y-axis and the lines y = a and y = 2a.
Draw a rough sketch of the region {(x, y) : y2 ≤ 5x, 5x2 + 5y2 ≤ 36} and find the area enclosed by the region using method of integration.
Draw a rough sketch and find the area of the region bounded by the two parabolas y2 = 4x and x2 = 4y by using methods of integration.
Prove that the area in the first quadrant enclosed by the x-axis, the line x = \[\sqrt{3}y\] and the circle x2 + y2 = 4 is π/3.
Find the area bounded by the curves x = y2 and x = 3 − 2y2.
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.
Using integration, find the area of the following region: \[\left\{ \left( x, y \right) : \frac{x^2}{9} + \frac{y^2}{4} \leq 1 \leq \frac{x}{3} + \frac{y}{2} \right\}\]
Find the area enclosed by the parabolas y = 4x − x2 and y = x2 − x.
In what ratio does the x-axis divide the area of the region bounded by the parabolas y = 4x − x2 and y = x2− x?
Find the area of the figure bounded by the curves y = | x − 1 | and y = 3 −| x |.
The area bounded by the curve y = loge x and x-axis and the straight line x = e is ___________ .
Area bounded by parabola y2 = x and straight line 2y = x is _________ .
The area bounded by the parabola y2 = 8x, the x-axis and the latusrectum is ___________ .
The area bounded by the y-axis, y = cos x and y = sin x when 0 ≤ x ≤ \[\frac{\pi}{2}\] is _________ .
The area of the circle x2 + y2 = 16 enterior to the parabola y2 = 6x is
Find the area bounded by the parabola y2 = 4x and the line y = 2x − 4 By using vertical strips.
Find the equation of the parabola with latus-rectum joining points (4, 6) and (4, -2).
The area enclosed by the circle x2 + y2 = 2 is equal to ______.
The area of the region bounded by the curve x = y2, y-axis and the line y = 3 and y = 4 is ______.
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 included between y2 = 9x and y = x
Find the area enclosed by the curve y = –x2 and the straight lilne x + y + 2 = 0
Compute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.
The area of the region bounded by the curve x2 = 4y and the straight line x = 4y – 2 is ______.
The area of the region bounded by the curve y = `sqrt(16 - x^2)` and x-axis is ______.
The area of the region enclosed by the parabola x2 = y, the line y = x + 2 and the x-axis, is
Find the area of the region bounded by the curve `y^2 - x` and the line `x` = 1, `x` = 4 and the `x`-axis.
Find the area of the region bounded by the curve `y = x^2 + 2, y = x, x = 0` and `x = 3`
Find the area of the region enclosed by the curves y2 = x, x = `1/4`, y = 0 and x = 1, using integration.
For real number a, b (a > b > 0),
let Area `{(x, y): x^2 + y^2 ≤ a^2 and x^2/a^2 + y^2/b^2 ≥ 1}` = 30π
Area `{(x, y): x^2 + y^2 ≥ b^2 and x^2/a^2 + y^2/b^2 ≤ 1}` = 18π.
Then the value of (a – b)2 is equal to ______.
Let P(x) be a real polynomial of degree 3 which vanishes at x = –3. Let P(x) have local minima at x = 1, local maxima at x = –1 and `int_-1^1 P(x)dx` = 18, then the sum of all the coefficients of the polynomial P(x) is equal to ______.
Find the area of the region bounded by the curve x2 = 4y and the line x = 4y – 2.
