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AP EAMCET · Maths · Indefinite Integration

\(g(x)\) is an anti derivative of \(f(x)=1+2^x \log 2\) and the graph of \(y=g(x)\) passes through \(\left(-1, \frac{1}{2}\right)\). Then the curve meets the \(\mathrm{Y}\) - axis at

  1. A \((0,1)\)
  2. B \((0,2)\)
  3. C \((0,-2)\)
  4. D \((1,1)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \((0,2)\)

Step-by-step Solution

Detailed explanation

\(f(x)=1+2^x \log 2\) \(\begin{aligned} & \Rightarrow \int f(x)=\int\left(1+2^x \log 2\right) d x \\ & \Rightarrow g(x)=x+\frac{2^x \log 2}{\log 2}+c\end{aligned}\) \(\Rightarrow \mathrm{g}(x)=x+2^x+c \Rightarrow y=x+2^x+c\) ...(i) Equation (i) passes through…