AP EAMCET · Maths · Definite Integration
The positive value of \(x\) satisfying the equation \(\int_x^1(1-t) d t=\frac{1}{2}\) is
- A \(1\)
- B \(\sqrt{2}\)
- C \(3\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \int_x^1(1-t) d t=\frac{1}{2} \Rightarrow\left[t-\frac{t^2}{2}\right]_x^1=\frac{1}{2} \\ & \Rightarrow\left[1-\frac{1}{2}-x+\frac{x^2}{2}\right]=\frac{1}{2} \\ & \Rightarrow \frac{1-2 x+x^2}{2}=\frac{1}{2} \Rightarrow(1-x)^2=1 \\ & \Rightarrow 1-x= \pm…
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