JEE Mains · Maths · STD 12 - 8. Application and integration
The area(in sq. units) of the region bounded by the curves \(y = 2^x\) and \(y = |x +1|\) in the first quadrant is
- A \(\frac {3}{2}\)
- B \({\log _e}\,2\, + \,\frac{3}{2}\)
- C \(\frac{3}{2} - \frac{1}{{{{\log }_e}\,2}}\)
- D \(\frac {1}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{3}{2} - \frac{1}{{{{\log }_e}\,2}}\)
Step-by-step Solution
Detailed explanation
Required Area \(\int\limits_0^1 {\left( {(x + 1) - {2^x}} \right)} dx\) \(=\left(\frac{x^{2}}{2}+x-\frac{2^{x}}{\ln 2}\right)_{0}^{1}\) \(=\left(\frac{1}{2}+1-\frac{2}{\ln 2}\right)-\left(0+0-\frac{1}{\ln 2}\right)\) \(=\frac{3}{2}-\frac{1}{\ln 2}\)
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