MHT CET · Maths · Indefinite Integration
If \(\mathrm{A}=\left[\begin{array}{lll}\mathrm{a} & 0 & 0 \\ 0 & \mathrm{~b} & 0 \\ 0 & 0 & \mathrm{c}\end{array}\right]\) where \(\mathrm{a}=7^{\mathrm{x}}, \mathrm{b}=7^{7^x}, \mathrm{c}=7^{7^{7^x}}\) then \(\int|A| \mathrm{d} x\), (Where \(|A|\) is the determinant of the matrix \(A\) ) is equal to
- A \(\frac{7^{7^x}}{(\log 7)^3}+k, \) where \(k\) is constant of integration
- B \(\frac{7^{7^{7^x}}}{\log 7}+\mathrm{k}, \) where k is constant of integration
- C \(\frac{7^{7^{7^x}}}{(\log 7)^3}+\mathrm{k} ,\) where k is constant of integration
- D \(7^{7^{7^x}}(\log 7)^3+\mathrm{k},\) where k is constant of integration
Answer & Solution
Correct Answer
(C) \(\frac{7^{7^{7^x}}}{(\log 7)^3}+\mathrm{k} ,\) where k is constant of integration
Step-by-step Solution
Detailed explanation
\(|A| = a \cdot b \cdot c = 7^x \cdot 7^{7^x} \cdot 7^{7^{7^x}}\) Let \(u = 7^{7^{7^x}}\).
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