tex]For JEE and NEET students[Easy Que's]...

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October 2022 1 35 Report

Evaluate :-

[tex]\bullet \: \underline{\displaystyle \sf \int\limits_{1}^{2} {e}^{(x + 4)} \: dx}[/tex]

[tex]\bullet \: \underline{\displaystyle \sf \int\limits_{1}^{2} \dfrac{dx}{(3x + 4)}}[/tex]

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EngrJohann

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$\Large \mathbb{SOLUTION:}$

$\begin{array}{l} \large \textsf{Evaluate:} \\ \\ \bullet \: \displaystyle \sf \int_1^2 {e}^{x + 4} \: dx = e^{x + 4} \Big |_1^2 = e^6 - e^5 = \boxed{\sf e^5(e - 1)} \\ \\ \begin{aligned} \bullet \: \displaystyle \sf \int_1^2 \frac{dx}{3x + 4} & \displaystyle \sf = \frac{1}{3} \int_1^2 \frac{3\: dx}{3x + 4} \\ \\ &\sf = \dfrac{1}{3} \ln(3x + 4) \Big |_1^2 \\ \\ & \sf = \dfrac{1}{3}(\ln 10 - \ln 7) \\ \\ &\sf = \boxed{\sf \dfrac{1}{3}\ln\left(\dfrac{10}{7}\right)} \end{aligned} \end{array}$

MystifiedBoy The Ln represents "Log" na?

EngrJohann Yes. Natural log or log of base e

MystifiedBoy Ok thanks!

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