Question 13 Marks
Find the area of the region bounded by the curve $y=4 x^2, Y$-axis and the lines $y=1, y=4$.
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Solve the Following Question.(3 Marks)
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Question 23 Marks
Find the area of the region bounded by the straight line 2y = 5x + 7, X-axis and x = 2, x = 5.
Question 33 Marks
Find the area of the region bounded by the parabola $y^2=x$ and the line $y=x$ in the first
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Find the area of the region bounded by the following curve, the X-axis and the given lines:
(i) 0 ≤ x ≤ 5, 0 ≤ y ≤ 2
(ii) y = sin x, x = 0, x = π
(iii) y = sin x, x = 0, x = $\frac{\pi}{3}$
(i) 0 ≤ x ≤ 5, 0 ≤ y ≤ 2
(ii) y = sin x, x = 0, x = π
(iii) y = sin x, x = 0, x = $\frac{\pi}{3}$
Answer
View full question & answer→Required area $=\int_0^5 y d x$, where $y =2$
$=\int_0^5 2 d x$
$=[2 x]_0^5$
$=2 \times 5-0$
$=10 \text { sq units. }$
$=\int_0^5 2 d x$
$=[2 x]_0^5$
$=2 \times 5-0$
$=10 \text { sq units. }$
Question 53 Marks
Find the area of sector bounded by the circle $x^2+y^2=16$ and the line $y=x$ in the first quadrant.
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Find the area of the region lying between the parabolas $y^2=4 a x$ and $x^2=4$ ay where $a>0$.
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Find the area of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.
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Using integration, find the area of the region bounded by the line $2 y+x=8, \mathrm{X}$-axis and the lines $x=2$ and $x=4$.
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Find the area enclosed between the $\mathrm{X}$-axis and the curve $y=\sin x$ for values of $x$ between 0 to $2 \pi$.
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Find the area bounded by the line $y=x, \mathrm{X}$ axis and the lines $x=-1$ and $x=4$.
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Find the area of the region bounded by the parabola:
View full question & answer→$y=4-x^2$ and the $X$-axis.
Question 123 Marks
Find the area of the region bounded by the parabola:
View full question & answer→$y^2=16 x$ and its latus rectum.