Advertisements
Advertisements
प्रश्न
Find the area under the given curve and given line:
y = x4, x = 1, x = 5 and x-axis
Advertisements
उत्तर
The curve y = x4 passes through the point (0, 0). The line OY is symmetric.
Now, y = x4
`dy/dx = 4x^3`
The sign of `dy/dx` changes from -ve to +ve when x moves through x = 0.
∴ x = 0 is the lowest point.
∴ Area of the region bounded by y = x4, x = 1, x = 5 and x-axis
= Area of the region PABQ
`= int_1^5 y dx = int_1^5 x^4 dx`
`= [x^5/5]_1^5 = [5^5/5 - 1/5]`
`= [5^4 - 1/5]`
`= 625 - 1/5`
`= (3125 - 1)/5`
`= 3124/5`
= 624.8 square unit
APPEARS IN
संबंधित प्रश्न
Find the area of the region bounded by the curve y2 = x and the lines x = 1, x = 4 and the x-axis.
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 enclosed between the parabola y2 = 4ax and the line y = mx
Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x + 12
Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).
Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Using integration, find the area of the region {(x, y) : x2 + y2 ≤ 1 ≤ x + y}.
Find the area of the region bounded by the parabola y2 = 16x and the line x = 4.
Find the area of the region bounded by the following curves, the X-axis and the given lines: y = x4, x = 1, x = 5
Choose the correct alternative :
Area of the region bounded by the curve x2 = y, the X-axis and the lines x = 1 and x = 3 is _______.
Area of the region bounded by y = x4, x = 1, x = 5 and the X-axis is _______.
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 _______.
The area of the region bounded by y2 = 4x, the X-axis and the lines x = 1 and x = 4 is _______.
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|`.
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 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.
The area of the shaded region bounded by two curves y = f(x), and y = g(x) and X-axis is `int_"a"^"b" "f"(x) "d"x + int_"a"^"b" "g"(x) "d"x`
The area of the circle x2 + y2 = 16 is ______
The area of the region x2 = 4y, y = 1 and y = 2 and the Y axis lying in the first quadrant is ______
Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8
Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
Find the area of the region bounded by the curve y = `sqrt(36 - x^2)`, the X-axis lying in the first quadrant and the lines x = 0 and x = 6
Find the area of the circle x2 + y2 = 62
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
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 ______.
The area of the region bounded by the curve y = x IxI, X-axis and the ordinates x = 2, x = –2 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`
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
Find the area between the two curves (parabolas)
y2 = 7x and x2 = 7y.
The area bounded by the curve | x | + y = 1 and X-axis is ______.
The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.
