The value of -23-1- x 2- dx is p - q in it-s simplest form- Then what p - q is

∫_ 2^3|1 x^2|dx=∫_ 2^ 1(x^2 1)dx+ ∫_ 1^1(1 x^2)dx+∫_1^3(x^2 1)dx = [x^3/3 x ]_ 2^ 1+ [ x x^3/3 ]_ 1^1+ [ x^3/3 x ]_1^3 =4/3+4/3+20/3=28/3 p/q = 28/3 p = 28, ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integration by Partial Fractions

The value of ...

Question

The value of $\int_{- 2}^{3} | 1 - x^{2} | d x$ is $\frac{p}{q}$ in it's simplest form. Then what $p + q$ is ___

Open in App

Solution

$\int_{- 2}^{3} | 1 - x^{2} | d x = \int_{- 2}^{- 1} (x^{2} - 1) d x + \int_{- 1}^{1} (1 - x^{2}) d x + \int_{1}^{3} (x^{2} - 1) d x$
$= {[\frac{x^{3}}{3} - x]}_{- 2}^{- 1} + {[x - \frac{x^{3}}{3}]}_{- 1}^{1} + {[\frac{x^{3}}{3} - x]}_{1}^{3}$
$= \frac{4}{3} + \frac{4}{3} + \frac{20}{3} = \frac{28}{3}$

$\frac{p}{q} = \frac{28}{3}$

$p = 28, q = 3$

$p + q = 31$

Suggest Corrections

Similar questions

Express in simplest

\frac{p}{q}

form and find the value

p + q

5. ¯ ¯ ¯ 2

Express in simplest

\frac{p}{q}

form and find the value

p + q

0.3 ¯ 4

Q. When the repeating decimal

10.363636

is written in simplest functional form

\frac{p}{q}

, find the value of

p + q

Q. 1.666666...... is a rational number and can be expressed in simplest

\frac{p}{q}

form. Then p + q is

We are given a set of first 100 naturals numbers. If the probability of the product of two numbers selected from this set be divisible by 7 is given by $\frac{p}{q}$ in it's simplest form. Then $\frac{p + q + 1}{p - 9}$ is ___

Join BYJU'S Learning Program

The value of ∫3−2|1−x2|dx is pq in it's simplest form. Then what p+q is ___

∫3−2|1−x2|dx=∫−1−2(x2−1)dx+∫1−1(1−x2)dx+∫31(x2−1)dx =[x33−x]−1−2+[x−x33]1−1+[x33−x]31 =43+43+203=283 pq=283 p=28,q=3 p+q=31

The value of $\int_{- 2}^{3} | 1 - x^{2} | d x$ is $\frac{p}{q}$ in it's simplest form. Then what $p + q$ is ___