Advertisements
Advertisements
Question
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5
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 in the first quadrant enclosed by x-axis, line x = `sqrt3` y and the circle x2 + y2 = 4.
The area between x = y2 and x = 4 is divided into two equal parts by the line x = a, find the value of a.
Find the area of the region bounded by the parabola y = x2 and y = |x| .
Find the area of the region bounded by the curve y2 = 4x and the line x = 3
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 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).
Find the area bounded by the circle x2 + y2 = 16 and the line `sqrt3 y = x` in the first quadrant, using integration.
Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9 "at" (-1,2sqrt2)`.
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
Area of the region bounded by x2 = 16y, y = 1 and y = 4 and the Y-axis, lying in the first quadrant is _______.
Using definite integration, area of the circle x2 + y2 = 49 is _______.
Solve the following :
Find the area of the region bounded by the curve y = x2 and the line y = 10.
Solve the following:
Find the area of the region bounded by the curve x2 = 25y, y = 1, y = 4 and the Y-axis.
Choose the correct alternative:
Area of the region bounded by the parabola y2 = 25x and the lines x = 5 is ______
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
The area of the circle x2 + y2 = 16 is ______
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 = 16
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
Area under the curve `y=sqrt(4x+1)` between x = 0 and x = 2 is ______.
Which equation below represents a parabola that opens upward with a vertex at (0, – 5)?
The equation of curve through the point (1, 0), if the slope of the tangent to t e curve at any point (x, y) is `(y - 1)/(x^2 + x)`, is
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 y = sec2x, x = `π/6`, x = `π/3` and x-axis is ______.
Find the area of the region lying in the first quadrant and bounded by y = 4x2, x = 0,y = 2 and y = 4.
