The area bounded by the curve y - x 3- x-axis and two ordinates x -1 to x -2 equal toA- 15-2 sq-unit-B- 15-4 sq-unit-C- 17-2 sq-unit-D- 17-4 sq-unit-

The correct option is B 15/4 sq. unit.Shaded area =∫_1^2ydx=∫_1^2x^3.dx=1/4[x^4]^2_1 A=1/4[16 1]=15/4 sq. unit. ...

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Standard XII

Mathematics

Double Ordinate of Ellipse

The area boun...

Question

The area bounded by the curve $y = x^{3}$ , x-axis and two ordinates x=1 to x=2 equal to

\frac{15}{2} s q . u n i t .

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\frac{15}{4} s q . u n i t .

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\frac{17}{2} s q . u n i t .

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\frac{17}{4} s q . u n i t .

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Solution

The correct option is B $\frac{15}{4} s q . u n i t .$
Shaded area = $\int_{1}^{2} y d x = \int_{1}^{2} x^{3} . d x = \frac{1}{4} [x^{4}]_{1}^{2}$

$A = \frac{1}{4} [16 - 1] = \frac{15}{4}$ sq. unit.

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Similar questions

Area bounded by the curve y = x³, the x-axis and the ordinates x = –2 and x = 1 is

A. – 9

Choose the correct answer
Area bounded by the curve $y = x^{3}$ , the X-axis the coordinates x = - 2 and x = 1 si
(a) -9 (b) $- \frac{15}{4}$
(c) $\frac{15}{4}$ (d) $\frac{17}{4}$

Q. I: The area bounded by the curve

y = x^{3}

and the ordinates

x = - 2

and

x = 1

with X-axis is

\frac{17}{4}

sq. units.
II: The area bounded by the parabola

y^{2} = x

and the straight line

y = 4

with Y-axis is

\frac{64}{3}

sq. units.
Which of the above statement is correct?

Q. The area(in sq.units) bounded by the curve

y = x^{3}, x -

axis and the two ordinates

x = - 2, x = 1

Area bounded by curve $y = x^{3}, x - a x i s$ axis and ordinates x=1 and x=4, is

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The area bounded by the curve y=x3, x-axis and two ordinates x=1 to x=2 equal to

The correct option is B 154sq.unit.Shaded area =∫21ydx=∫21x3.dx=14[x4]21 A=14[16−1]=154 sq. unit.

The area bounded by the curve $y = x^{3}$ , x-axis and two ordinates x=1 to x=2 equal to

The correct option is B $\frac{15}{4} s q . u n i t .$
Shaded area = $\int_{1}^{2} y d x = \int_{1}^{2} x^{3} . d x = \frac{1}{4} [x^{4}]_{1}^{2}$

$A = \frac{1}{4} [16 - 1] = \frac{15}{4}$ sq. unit.