₀^{4}≤ft|x-1|dx - NCERT Class XII Mathematics Chapter -

NCERT Class XII Mathematics Chapter - - Solutions

Exercise - 7.11
By using the properties of definite integrals, evaluate the integrals in Exercises 208 to 225.

Question : 224 of 271

Marks: +1, -0

\int\limits_{0}^{4}\left|x-1\right|dx

Solution:

Let

I=\int\limits_{0}^{4}\left|x-1\right|dx

Define

\left|x-1\right| = \begin{cases} -(x-1), & \text{if } (x-1) < 0 \text{ or } x < 1 \\ x-1, & \text{if } (x-1) \ge 0 \text{ or } x \ge 1 \end{cases}

\therefore I = -\int\limits_{0}^{1}(x-1)dx + \int\limits_{1}^{4}(x-1)dx

=-\left[\frac{(x-1)^2}{2}\right]_{0}^{1}+\left[\frac{(x-1)^2}{2}\right]_{1}^{4}

=-\frac{1}{2}[0-1]+\frac{1}{2}[9-0]

=\frac{1}{2}+\frac{9}{2}=5

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