- x6sin5x7dx-k-5cos5x7-c- then k-

The correct option is D 1/7 ∫ x^6sin(5x^7)dx =x^7=t 7x^6dx=dt x^6dx=dt7 ∫ sin(5t)dt7 = 17∫ sin(5t)dt ∵∫ sin t dt= cos t+c ...

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Standard XII

Mathematics

Special Integrals - 1

∫ x6sin5x7dx=...

Question

$\int x^{6} sin (5 x^{7}) d x = \frac{k}{5} cos (5 x^{7}) + c,$
then $k =$

7

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- 7

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\frac{1}{7}

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\frac{- 1}{7}

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Solution

The correct option is D $\frac{- 1}{7}$
$\int x^{6} s i n (5 x^{7}) d x$
$= x^{7} = t$
$7 x^{6} d x = d t$
$x^{6} d x = \frac{d t}{7}$
$\int s i n (5 t) \frac{d t}{7} = \frac{1}{7} \int s i n (5 t) d t$
$∵ \int s i n t d t = - c o s t + c = \frac{1}{7} - \frac{c o s (5 t)}{5} + c$
$= \frac{(\frac{1}{7})}{- 5} c o s (5 t) + c$
Hence, the value of $k = (\frac{- 1}{7})$ .

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∫x6sin(5x7)dx=k5cos(5x7)+c, then k=

The correct option is D −17∫x6sin(5x7)dx=x7=t7x6dx=dtx6dx=dt7∫sin(5t)dt7=17∫sin(5t)dt∵∫sintdt=−cost+c=17−cos(5t)5+c=(17)−5cos(5t)+cHence, the value of k=(−17).

$\int x^{6} sin (5 x^{7}) d x = \frac{k}{5} cos (5 x^{7}) + c,$
then $k =$