SATHEE: Indefinite Integration 3 Question 3

Indefinite Integration 3 Question 3

3. The intercepts on $X$ -axis made by tangents to the curve, $y = \int_{0}^{x} | t | d t, x \in R$ , which are parallel to the line $y = 2 x$ , are equal to

(2013 Main)

(a) \pm 1

(b) \pm 2

(d) \pm 4

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Answer:

Correct Answer: 3. (a)

Solution:

Given, $y = \int_{0}^{x} | t | d t$

$∴ \frac{d y}{d x} = | x | \cdot 1 - 0 = | x |$ [by Leibnitz’s rule]

$∵$ Tangent to the curve $y = \int_{0}^{x} | t | d t, x \in R$ are parallel to the line $y = 2 x$

$∴$ Slope of both are equal $\Rightarrow x = \pm 2$

Points, $y = \int_{0}^{\pm 2} | t | d t = \pm 2$

Equation of tangent is

$y - 2 = 2 (x - 2) and y + 2 = 2 (x + 2)$

For $x$ intercept put $y = 0$ , we get

$0 - 2 = 2 (x - 2) and 0 + 2 = 2 (x + 2)$

$\Rightarrow x = \pm 1$

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Indefinite Integration 3 Question 3

3. The intercepts on X-axis made by tangents to the curve, y=∫0x|t|dt,x∈R, which are parallel to the line y=2x, are equal to

Answer:

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3. The intercepts on $X$ -axis made by tangents to the curve, $y = \int_{0}^{x} | t | d t, x \in R$ , which are parallel to the line $y = 2 x$ , are equal to