Advertisements
Advertisements
Question
Find the area of the region bounded by the curve 4y = 7x + 9, the X-axis and the lines x = 2 and x = 8
Solution
Let A be the required area.
Given equation of the curve is 4y = 7x + 9
i.e., y = `(7x + 9)/4`
∴ A = `int_2^8 y "d"x`
= `int_2^8 (7x + 9)/4 "d"x`
= `1/4 int_2^8 (7x + 9) "d"x`
= `1/4[7(x^2/2) + 9x]_2^8`
= `1/4[[7(8^2/2) + 9(8) - 7(2^2/2) + 9(2)]]`
= `1/4[224 + 72 - (14 + 18)]`
= `1/4(296 - 32)`
= `1/4(264)`
∴ A = 66 sq.units
APPEARS IN
RELATED QUESTIONS
Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`
Find the area enclosed between the parabola y2 = 4ax and the line y = mx
Find the area of the smaller region bounded by the ellipse `x^2/9 + y^2/4` and the line `x/3 + y/2 = 1`
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
Fill in the blank :
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 _______.
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.
State whether the following statement is True or False:
The area of portion lying below the X axis is negative
The area of the region bounded by y2 = 25x, x = 1 and x = 2 the X axis is ______
Find area of the region bounded by the parabola x2 = 36y, y = 1 and y = 4, and the positive Y-axis
If `int_0^(pi/2) log (cos x) "dx" = - pi/2 log 2,` then `int_0^(pi/2) log (cosec x)`dx = ?
The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______
The area of the region bounded by the X-axis and the curves defined by y = cot x, `(pi/6 ≤ x ≤ pi/4)` is ______.
The area enclosed by the parabolas x = y2 - 1 and x = 1 - y2 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
The area enclosed by the parabola x2 = 4y and its latus rectum is `8/(6m)` sq units. Then the value of m is ______.
