Advertisements
Advertisements
Question
State whether the following statement is True or False:
The area bounded by the curve y = f(x) lies on the both sides of the X-axis is `|int_"a"^"b" "f"(x) "d"x| + |int_"b"^"c" "f"(x) "d"x|`
Options
True
False
Solution
True
APPEARS IN
RELATED QUESTIONS
Find the area of the region in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is ______.
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.
Find the area of the region bounded by the following curves, the X-axis and the given lines:
y = x2 + 1, x = 0, x = 3
Using definite integration, area of the circle x2 + y2 = 49 is _______.
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|`.
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 y = x2 and the line y = 10.
The area bounded by the parabola x2 = 9y and the lines y = 4 and y = 9 in the first quadrant is ______
The area of the circle x2 + y2 = 16 is ______
Find the area of the region bounded by the parabola y2 = 25x and the line x = 5
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.
The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 is ______.
Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
The area of the circle `x^2 + y^2 = 16`, exterior to the parabola `y = 6x`
If area of the region bounded by y ≥ cot( cot–1|In|e|x|) and x2 + y2 – 6 |x| – 6|y| + 9 ≤ 0, is λπ, then λ is ______.
If the area enclosed by y = f(x), X-axis, x = a, x = b and y = g(x), X-axis, x = a, x = b are equal, then f(x) = g(x).
