Solve - - 12 x4 - 12 dx - - - 12 x24 dx

The correct option is C 98 A= ∫_1^2( x4 + 12) dx ∫_ 1^2x^24 dx =( x^28 + x2)^2 ( x^312 #160; #160;)^2 = ( 12 +1 18+ 12) ( 23 + 11 ...

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Byju's Answer

Standard XII

Mathematics

Rationalization Method to Remove Indeterminate Form

Solve ∫ - 1...

Question

Solve $2 \int - 1 (\frac{x}{4} + \frac{1}{2}) d x - 2 \int - 1 \frac{x^{2}}{4} d x$

\frac{5}{8}

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\frac{- 9}{8}

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\frac{9}{8}

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\frac{1}{8}

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Solution

The correct option is C $\frac{9}{8}$
$A = \int_{1}^{2} (\frac{x}{4} + \frac{1}{2}) d x - \int_{- 1}^{2} \frac{x^{2}}{4} d x$
$= {(\frac{x^{2}}{8} + \frac{x}{2})}^{2} - {(\frac{x^{3}}{12})}^{2}$
$= (\frac{1}{2} + 1 - \frac{1}{8} + \frac{1}{2}) - (\frac{2}{3} + \frac{1}{12})$
$= (2 - \frac{1}{8}) - (\frac{3}{4})$
$= \frac{15}{8} - \frac{6}{8}$
$= \frac{9}{8}$

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Similar questions

Q. Solve

\frac{7}{8} + \frac{5}{12} \times \frac{9}{10} - \frac{1}{4}

Q. Which of the following will come next in the following series?

919829873987649876559876546987654

Fill in the blanks:

$(i) - 4 \times \frac{7}{9} = \frac{7}{9} \times$ ___

$(i i) \frac{5}{11} \times \frac{- 3}{8} = \frac{- 3}{8} \times$ ___

$(i i i) \frac{1}{2} \times (\frac{3}{4} + \frac{- 5}{12}) = \frac{1}{2} \times$ ____ $+ (\times) \frac{- 5}{12}$

$(i v) \frac{- 4}{5} \times \frac{5}{7} \times$ ___ $= (\frac{- 4}{5} \times \frac{5}{7}) \times \frac{- 8}{9}$

Q. Solve:

1 \frac{4}{5} - 2 \frac{3}{4}

\frac{8}{11} + \frac{3}{8} + \frac{9}{10}

$Name the multiplication property of rational numbers shown below: (i) \frac{3}{5} \times \frac{- 8}{9} = \frac{- 8}{9} \times \frac{3}{5} (i i) \frac{- 3}{4} \times (\frac{5}{7} \times \frac{- 8}{15}) = (\frac{- 3}{5} \times \frac{5}{7}) \times \frac{- 8}{15} (i i i) \frac{4}{5} \times (\frac{3}{- 8} + \frac{- 4}{7}) = \frac{4}{5} \times \frac{3}{- 8} + \frac{4}{5} \times \frac{- 4}{7} (i v) \frac{- 7}{5} \times \frac{5}{- 7} = 1 (v) \frac{8}{- 9} \times 1 = 1 \times \frac{8}{- 9} = \frac{8}{- 9} (v i) \frac{- 3}{4} \times 0 = 0$

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Solve 2∫−1(x4+12)dx−2∫−1x24dx

The correct option is C 98A=∫21(x4+12)dx−∫2−1x24dx=(x28+x2)2−(x312)2=(12+1−18+12)−(23+112)=(2−18)−(34)=158−68=98

Solve $2 \int - 1 (\frac{x}{4} + \frac{1}{2}) d x - 2 \int - 1 \frac{x^{2}}{4} d x$