COMEDK · Maths · 28. Indefinite Integration
\(\int 7^{2 x} d x=\varphi(x)+c\) then \(\varphi(x)=\)
- A \(7^{2 x} \log 7\)
- B \(\dfrac{7^{2 x}}{2 \log 7}\)
- C 1
- D \(\dfrac{7^{2 x}}{\log 7}\)
Answer & Solution
Correct Answer
(B) \(\dfrac{7^{2 x}}{2 \log 7}\)
Step-by-step Solution
Detailed explanation
The integral to be evaluated is \(I = \int 7^{2x} dx\). Using the standard integration formula \(\int a^{u} du = \dfrac{a^{u}}{\ln a} + c\), where \(a = 7\) and \(u = 2x\). Since \(u = 2x\), \(du = 2 dx\), which implies \(dx = \dfrac{du}{2}\). Substituting these into the…
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