Question

Find the area of the region under the curve

* y* =

from

* x* = 0

to

* x* = 3.

Answer #1

**Given**

**To find the area under this curve from x=0 to x=3 we
need to find the integral of the curve that
is**

**Let **

**Putting these values**

** **

**substituting u=5x back**

**by evaluating the limits**

By putting the values

**Hence the area under the curve from
is **

1.Find the area of the region between the curves y= x(1-x) and y
=2 from x=0 and x=1.
2.Find the area of the region enclosed by the curves
y=x2 - 6 and y=3 between their
interaction.
3.Find the area of the region bounded by the curves
y=x3 and y=x2 between their interaction.
4. Find the area of the region bounded by y= 3/x2 ,
y= 3/8x, and y=3x, for x greater than or equals≥0.

Find the area of the region bounded by the y-axis, the curve y =
ln(x+ 1),
and the tangent line to y = ln(x + 1) at x = 3.

1. Find the area of the region enclosed between y=4sin(x) and
y=4cos(x) from x=0 to x=0.5π
2. Find the volume of the solid formed by rotating the region
enclosed by
x=0, x=1, y=0, y=8+x^5
about the x-axis.
3. Find the volume of the solid obtained by rotating the region
bounded by
y=x^2, y=1.
about the line y=7.

4. Find the area of the region bounded by the curve y = 4 − x 2
and the line y = x + 2.

Find the area of the region enclosed by the curve x = 8cos(t) −
4sin(2t), y = 5sin(t) with 0 ≤ t ≤ 2 π

Find the area of the region enclosed between y=4sin(x) and
y=4cos(x) from x=0 to x=0.4π. Hint: Notice that this region
consists of two parts.

(1 point) Find the area of the region enclosed between y=3sin(x)
and y=3cos(x) from x=0 to x=0.6π. Hint: Notice that this region
consists of two parts.

. Find the area of the region that is enclosed between the curve
by y = x2 and y = x + 6.
Hint: Use
ab [ f (x) – g
(x) ] dx, where f (x) =
x2 and g (x) = x +6,
f (x) > g (x).
OR
Reduce the equation of straight line into symmetric form, the
equations
x + 3y – z + 5 = 0, 2y +
z = 3, also find...

Find the area of the region that is enclosed between y= 4sin(x)
and y= 3cos(x) from x=0 to x=0.3π

Find the area of the region bounded by the curves x+y^2= 2 and
x+y=0

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