Advertisements
Advertisements
प्रश्न
Sketch the graph of y = |x + 3| and evaluate `int_(-6)^0 |x + 3|dx`
Advertisements
उत्तर
y = |x + 3|
At x = -3, y = 0
AQ is the line y = x + 3
When x + 3 < 0,
y = -(x + 3) = -x – 3
The graph of the line AP is AP.
∴ y =|x + 3| is shown in the graph.
`int_(-6)^1 |x + 3| dx`
`= int_(- 6)^(-3) |- x - 3| dx + int_(-3)^0 (x + 3) dx`
`= [- x^2/2 - 3x]_(-6)^(-3) + [x^2/2 + 3x]_(- 3)^0`
`= - [x^2/2 + 3x]_(- 6)^(- 3) + [x^2/2 + 3x]_(-3)^0`
`= - [x^2/2 + 3x]_(-6)^(-3) + [x^2/2 + 3x]_(-3)^0`
`= - [(9/2 - 9) - (36/2 - 18) + 0 - (9/2 - 9)]`
`= - [- 9/2 - 0] + 9/2`
`= 9/2 + 9/2`
= 9 square unit
APPEARS IN
संबंधित प्रश्न
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 curve y2 = x and the lines x = 1, x = 4 and the x-axis.
Find the area of the region bounded by the ellipse `x^2/16 + y^2/9 = 1.`
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 curve y2 = 4x and the line x = 3
Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.
Find the area enclosed between the parabola y2 = 4ax and the line y = mx
Find the area enclosed between the parabola 4y = 3x2 and the straight line 3x - 2y + 12 = 0.
Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`
Draw a rough sketch and find the area bounded by the curve x2 = y and x + y = 2.
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: y = x4, x = 1, x = 5
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
Find the area of the region bounded by the following curves, the X-axis and the given lines:
y = x2 + 1, x = 0, x = 3
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 _______.
Find the area of the region bounded by y = x2, the X-axis and x = 1, x = 4.
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 curve y = x3, x = 1, x = 4 and the X-axis is ______
Choose the correct alternative:
Area of the region bounded by x = y4, y = 1 and y = 5 and the Y-axis lying in the first quadrant is ______
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`
Find area of the region bounded by the curve y = – 4x, the X-axis and the lines x = – 1 and x = 2
Find the area of the circle x2 + y2 = 62
The area enclosed between the curve y = loge(x + e) and the coordinate axes is ______.
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)?
Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is:
The slope of a tangent to the curve y = 3x2 – x + 1 at (1, 3) is ______.
The area (in sq.units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is ______.
The area of the region bounded by the curve y = sin x and the x-axis in [–π, π] is ______.
Area in first quadrant bounded by y = 4x2, x = 0, y = 1 and y = 4 is ______.
Area bounded by the curves y = `"e"^(x^2)`, the x-axis and the lines x = 1, x = 2 is given to be α square units. If the area bounded by the curve y = `sqrt(ℓ "n"x)`, the x-axis and the lines x = e and x = e4 is expressed as (pe4 – qe – α), (where p and q are positive integers), then (p + q) is ______.
The area bounded by the x-axis and the curve y = 4x – x2 – 3 is ______.
The area bounded by the curve `y = 3/2sqrtx`, the line x = 1 and x-axis is ______ sq. units.
