-0-10sec-2-3x-6-dx-None of these-

The correct option is C None of these I=∫_0^10sec^2(3x+6)dx Let 3x+6=u ⇒ 3dx=du⇒ dx=du/3 I=∫ sec^2u du/3 =1/3tan(u)+c I=1/3 tan(3x+6)^10_0 1/3[tan36 tan6] ...

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Byju's Answer

Standard XII

Physics

Definite Integrals

∫_0^10sec^2(3...

Question

$\int_{0}^{10} s e c^{2} (3 x + 6) d x$

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None of these

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Solution

The correct option is D
None of these

$I = \int_{0}^{10} s e c^{2} (3 x + 6) d x$

Let $3 x + 6 = u$

$\Rightarrow 3 d x = d u \Rightarrow d x = \frac{d u}{3}$

$I = \int s e c^{2} u \frac{d u}{3}$

= $\frac{1}{3} t a n (u) + c$
$I = \frac{1}{3} t a n (3 x + 6)_{0}^{10}$
$\frac{1}{3} [t a n 36 - t a n 6]$

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$\int_{0}^{10} s e c^{2} (3 x + 6) d x$

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∫100sec2(3x+6)dx

The correct option is D None of these I=∫100sec2(3x+6)dx Let 3x+6=u ⇒3dx=du⇒dx=du3 I=∫sec2udu3 =13tan(u)+c I=13tan(3x+6)100 13[tan36−tan6]

$\int_{0}^{10} s e c^{2} (3 x + 6) d x$