Advertisements
Advertisements
Question
Choose the correct alternative :
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _____.
Options
`(3142)/(5)"sq.unts"`
`(3124)/(5)"sq.unts"`
`(3142)/(3)"sq.unts"`
`(3124)/(3)"sq.unts"`
Advertisements
Solution
Let A be the required area.
Consider the equation y = x4.
∴ A = `int_1^5 y*dx`
= `int_1^5 x^4*dx`
= `[(x^5)/5]_1^5`
= `(1)/(5)[x^5]_1^5`
= `(1)/(5)[(5)^5 - (1)^5]`
= `(1)/(5)(3125 - 1)`
∴ A = `(3124)/(5)"sq . units"`.
APPEARS IN
RELATED QUESTIONS
Using integration find the area of the region {(x, y) : x2+y2⩽ 2ax, y2⩾ ax, x, y ⩾ 0}.
Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle
`x^2+y^2=4 at (1, sqrt3)`
Find the area of the region bounded by the ellipse `x^2/16 + y^2/9 = 1.`
Find the area of the smaller part of the circle x2 + y2 = a2 cut off by the line `x = a/sqrt2`
Find the area under the given curve and given line:
y = x2, x = 1, x = 2 and x-axis
Find the area of the smaller region bounded by the ellipse `x^2/a^2 + y^2/b^2 = 1` and the line `x/a + y/b = 1`
Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = `sqrt(16 - x^2)`, x = 0, x = 4
Find the area of the region bounded by the following curves, the X-axis and the given lines: 2y + x = 8, x = 2, x = 4
Fill in the blank :
Area of the region bounded by x2 = 16y, y = 1, 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 _______.
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
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.
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
Choose the correct alternative:
Using the definite integration area of the circle x2 + y2 = 16 is ______
The area of the region lying in the first quadrant and bounded by the curve y = 4x2, and the lines y = 2 and y = 4 is ______
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 is ______.
The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is ______.
Area bounded by y = sec2x, x = `π/6`, x = `π/3` and x-axis is ______.
The figure shows as triangle AOB and the parabola y = x2. The ratio of the area of the triangle AOB to the area of the region AOB of the parabola y = x2 is equal to ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
Which strips are considered for the area bounded by \[y=f(x)\], the \[x\]-axis, and the ordinates \[x=a\] and \[x=b\]?
What is the area of an elementary horizontal strip of length \[x\] and infinitesimally small width \[dy\]?
Which integral gives the area bounded by \[x=g(y)\], the \[y\]-axis, and the horizontal lines \[y=c\] and \[y=d\]?
Which expression gives physical area when the curve \[y=f(x)\] lies below the \[x\]-axis from \[x=a\] to \[x=b\]?
