Plus Two Maths Application of Integrals Four Mark Questions and Answers
Question 1.
Consider the following figure.
- Find the point of intersection (P) of the given parabola and the line. (2)
- Find the area of the shaded region. (2)
Answer:
1. We have, y = x2 and y = x ⇒ x = x2 ⇒
⇒ x2 – x = 0 ⇒ x(x – 1) = 0 ⇒ x = 0, 1
When x = 0, y =0 and x = 1, y = 1.
Therefore the points of intersections are (0, 0) and(1, 1).
2. Required area
Question 2.
1. Find the point of intersection ‘p’ of the given parabola and the line. (2)
2. Find the area of the shaded region. (2)
Answer:
1. Given, y = x2, y = 2x
⇒ 2x = x2 ⇒ x2 – 2x = 0 ⇒ x(x – 2) = 0 ⇒ x = 0, 2
We have, y = 2x
⇒ when x = 0 ⇒ y = 0, when x = 2 ⇒ y = 4
‘P’ has co-ordinate (2, 4)
Plus Two Maths Application of Integrals Six Mark Questions and Answers
Question 1.
- Draw the graph of y2 = 4x and y = x. (2)
- Find the points of intersection of y2 = 4x and y = x. (2)
- Find the area bounded by the graphs.(2)
Answer:
1. y2 = 4x is a parabola and y = x is a straight line passing through the origin.
Therefore verified
Question 4.
The figure given below contains a straight line L with slope √8 and a circle.
