# Plus Two Maths Chapter Wise Previous Questions Chapter 8 Application of Integrals

Kerala State Board New Syllabus Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 8 Application of Integrals.

## Kerala Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 8 Application of Integrals

### Plus Two Maths Application of Integrals 4 Marks Important Questions

Question 1.
(i) The area bounded by the curve y = f(x) x-axis and the line x= a and x= b is……
(ii) Find the area enclosed between the Parabola y = x2 and the straight line 2x – y + 3 = 0 (March – 2010)

Question 2.
Find the area enclosed between the curve x2 = 4y and the line x = 4y – 2 (March -2011)

Question 3.
(i) Area of the shaded portion in the figure is equal to

(ii) Consider the curves y = x2, x = 0, y = 1, y = 4.
Draw a rough sketch and shade the region bounded by these curves, Find area of the shaded region.

Question 4.
Consider the following figure:

(i) Find the point of Intersection P of the circle x2 + y2 = 32 and the line y = x.
(ii) Find the area of the shaded region. (EDUCATE – 2017; March – 2013; March – 2014)

Question 5.
(a) The area bounded by the curve, above the x-axis, between x = a and x = b is

(b) Find the area of the circle x2 + y2 = 4 using integration. (March – 2016)

Question 6.
(i) The area bounded by y = 2cosx , the x-axis from x = 0 to x = $$\frac{\pi}{2}$$ is
(a) 0
(b) 1
(c) 2
(d) -1
(ii) Find the area of the region bounded by the y2 = 4ax and x2 = 4ay, a > 0 (March – 2017)

When x = 4a, y = 4a and x = 0, y = 0.
Therefore the point is (0, 0) and (4a, 4a).

### Plus Two Maths Application of Integrals 6 Marks Important Questions

Question 1.
Consider the circle x2 + y2 = 16 and the straight line $$y=\sqrt{3} x$$ as shown ¡n the figure

(i) Find the points A and B as shown in the figure.
(ii) Find the area of the shaded region in the figure using definite integral. (May -2010)
(i) The point of intersection of x2 + y= l6 and

Question 2.
(i) Draw the rough sketch of $$\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$$
(ii) Find the area bounded by the above curve using integration. (May – 2011)
(i) The curve is an ellipse.

Question 3.
(i) Find the area enclosed between the curve y2 = x, x = 1, x = 4 and x-axis.
(ii) Using ntegration, find the area of the region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1). (March-2012)

Required area ΔABC = Area ΔAB2
+ Area 2BC3 – Area ΔAC3
Equation AC is y = 2(x – 1)
Equation BC is y = 4 – x
Equation AB is y = 1/2 (x – 1)

Question 4.

Using the above figure
Find the equation of AB.
Findthe point P.
Find the area of the shaded region by integration. (May – 2013)
(i) The equation of a line passing through (0,2)

Question 5.
Consider the ellipse $$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$$ and the line $$\frac{x}{3}+\frac{y}{2}=1$$.
(a) Find the points where the line intersects the ellipse?
(b) Shade the smaller region bounded by the ellipse and the line.
(c) Find the area of the shaded region. (May – 2014)

Question 6.
Consider the function f(x) = |x| + 1; g(x) = 1 – |x|
(a) Sketch the graph and shade the enclosed region between them.
(b) Find the area of the shaded region. (March – 2015)