Advertisements
Advertisements
Question
The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is ______.
Options
`1/2` log 2 sq units
log 2 sq units
2 log 2 sq units
3·log 2 sq units
Advertisements
Solution
The area bounded by the curve y = tan x, X-axis and the line x = `pi/(4)` is `bbunderline(1/2 log 2 "sq units")`.
Explanation:
Required area = `int_0^(pi/4) tan dx`
= `log |sec x|_0^(pi/4)`
= `log sqrt2`
= `1/2` log 2 sq units.
APPEARS IN
RELATED QUESTIONS
Find the area of the region bounded by the following curves, X-axis and the given lines: y = 2x, x = 0, x = 5
Find the area of the region bounded by the following curves, X-axis and the given lines: x = 2y, y = 0, y = 4
Find the area of the region bounded by the parabola y2 = 16x and its latus rectum.
Find the area of the region bounded by the parabola: y = 4 – x2 and the X-axis.
Find the area of the region included between y2 = 2x and y = 2x.
Find the area of the region included between: y2 = 4x, and y = x
Find the area of the region included between: y = x2 and the line y = 4x
Choose the correct option from the given alternatives :
The area of the region bounded between the line x = 4 and the parabola y2 = 16x is ______.
Choose the correct option from the given alternatives :
The area bounded by the parabola y2 = 8x, the X-axis and the latus rectum is
Choose the correct option from the given alternatives :
The area of the circle x2 + y2 = 25 in first quadrant is
Choose the correct option from the given alternatives :
The area of the region bounded by the ellipse `x^2/a^2 + y^2/b^2` = 1 is
Choose the correct option from the given alternatives :
The area enclosed between the curve y = cos 3x, 0 ≤ x ≤ `pi/(6)` and the X-axis is
Choose the correct option from the given alternatives :
The area enclosed between the two parabolas y2 = 4x and y = x is
Choose the correct option from the given alternatives :
The area of the region bounded by x2 = 16y, y = 1, y = 4 and x = 0 in the first quadrant, is
Choose the correct option from the given alternatives :
The area of the region included between the line x + y = 1 and the circle x2 + y2 = 1 is
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = π
Solve the following :
Find the area of the region bounded by the following curve, the X-axis and the given lines : y = sin x, x = 0, x = `pi/(3)`
Solve the following:
Find the area of the region lying between the parabolas: 4y2 = 9x and 3x2 = 16y
Solve the following :
Find the area of the region lying between the parabolas : y2 = x and x2 = y.
Solve the following :
Find the area of the region bounded by the curve (y – 1)2 = 4(x + 1) and the line y = (x – 1).
The area of the region bounded by the ellipse x2/64 + y2/100 = 1, is ______ sq.units
The area bounded by the parabola y2 = x along the X-axis and the lines x = 0, x = 2 is ______ sq.units
The area bounded by the curve y2 = x2, and the line x = 8 is ______
The area bounded by the parabola y2 = 32x the X-axis and the latus rectum is ______ sq.units
The area bounded by the ellipse `x^2/4 + y^2/25` = 1 and the line `x/2 + y/5` = 1 is ______ sq.units
Find the area bounded by the curve y2 = 36x, the line x = 2 in first quadrant
Find the area bounded by the curve y = sin x, the lines x = 0 and x = `pi/2`
Find the area of the region bounded by the parabola y2 = 32x and its Latus rectum in first quadrant
Find the area of the region bounded by the curve y2 = 8x, the X−axis and the given lines x = 1, x = 3, y ≥ 0
Find the area of the region bounded by the curve x2 = 12y, the Y−axis and the given lines y = 2, y = 4, x ≥ 0
Using integration, find the area of the region bounded by the line 2y + x = 8 , X−axis and the lines x = 2 and x = 4
Find the area of the region bounded by the parabola x2 = 4y and The X-axis and the line x = 1, x = 4
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 curves x2 = 8y, y = 2, y = 4 and the Y-axis, lying in the first quadrant
Find the area of the sector bounded by the circle x2+ y2 = 16, and the line y = x in the first quadrant
The area bounded by the curve y = x3, the X-axis and the Lines x = –2 and x = 1 is ______.
Find the area of the region bounded by the curve y2 = 4x, the X-axis and the lines x = 1, x = 4 for y ≥ 0.
Find the area of the region bounded by the curve y = x2 and the line y = 4.
Find the area common to the parabola y2 = x – 3 and the line x = 5.
Find the area bounded by the lines y = 5x – 10, X-axis and x = 5.
Find the area of the region bounded by the curve y = x2, and the lines x = 1, x = 2, and y = 0.
