Advertisements
Advertisements
Question
Using definite integration, area of the circle x2 + y2 = 49 is _______.
Advertisements
Solution
Using definite integration, area of the circle x2 + y2 = 49 is 49π sq.units.
Explanation:
Area of the circle x2 + y2 = r2 is πr2 sq.units.
Here, r2 = 49
∴ Required area = 49π sq.units.
RELATED QUESTIONS
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
Find the area of the region enclosed by the parabola x2 = y, the line y = x + 2 and x-axis
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).
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
Fill in the blank :
The area of the region bounded by the curve x2 = y, the X-axis and the lines x = 3 and x = 9 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`
State whether the following is True or False :
The area bounded by the two cures y = f(x), y = g (x) and X-axis is `|int_"a"^"b" f(x)*dx - int_"b"^"a" "g"(x)*dx|`.
Solve the following :
Find the area of the region bounded by the curve xy = c2, the X-axis, and the lines x = c, x = 2c.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
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
Find area of the region bounded by 2x + 4y = 10, y = 2 and y = 4 and the Y-axis lying in the first quadrant
Find the area of the circle x2 + y2 = 62
Find the area of the circle x2 + y2 = 16
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
The ratio in which the area bounded by the curves y2 = 8x and x2 = 8y is divided by the line x = 2 is ______
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
Area of the region bounded by y= x4, x = 1, x = 5 and the X-axis is ______.
Area bounded by the curves y = `"e"^(x^2)`, the x-axis and the lines x = 1, x = 2 is given to be α square units. If the area bounded by the curve y = `sqrt(ℓ "n"x)`, the x-axis and the lines x = e and x = e4 is expressed as (pe4 – qe – α), (where p and q are positive integers), then (p + q) is ______.
Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis is ______.
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 region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
Which expression gives physical area when the curve \[y=f(x)\] lies below the \[x\]-axis from \[x=a\] to \[x=b\]?
Which antiderivative is used in evaluating \[\int \sqrt{a^2-x^2}\,dx\] for the ellipse area?
