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Question
Solve the following :
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
Solution
Required area = `int_1^4y*dx`
= `int_1^4 x^2*dx`
= `[x^3/3]_1^4`
= `(1)/(3)(4^3 - 1^3)`
= `(1)/(3)(64 - 1)`
= `(1)/(3)(63)`
= 21 sq. units.
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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 curve y = f(x), X-axis and lines x = a and x = b is `|int_"a"^"b" f(x)*dx|`.
If the curve, under consideration, is below the X-axis, then the area bounded by curve, X-axis and lines x = a, x = b is positive.
Choose the correct alternative:
Area of the region bounded by x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______
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|`
The area of the region bounded by the curve y2 = 4x, the X axis and the lines x = 1 and x = 4 is ______
The area of the region bounded by the curve y = 4x3 − 6x2 + 4x + 1 and the lines x = 1, x = 5 and X-axis is ____________.
`int "e"^x ((sqrt(1 - x^2) * sin^-1 x + 1)/sqrt(1 - x^2))`dx = ________.
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
The area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.
