TS EAMCET · Maths · Definite Integration
If \(f(x)=\int_1^x \frac{1}{2+t^4} d t\), then
- A \(\frac{1}{18} < f(2) < \frac{1}{3}\)
- B \(f(2) < \frac{1}{2}\) (or) \(f(2)>2\)
- C \(f(2) < \frac{1}{3}\)
- D \(f(2)>\frac{1}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{18} < f(2) < \frac{1}{3}\)
Step-by-step Solution
Detailed explanation
We have, \[ f(x)=\int_1^x \frac{1}{2+t^4} d t \] So, \(f(2)=\int_1^2 \frac{1}{2+t^4} d t\) Now, \(f(2)>\int_1^2 \min \left(\frac{1}{2+t^4}\right) d t \quad>\int_1^2 \frac{1}{2+2^4} d t\) \[ >\int_1^2 \frac{1}{18} d t \quad \Rightarrow \quad f(2)>\frac{1}{18} \] and…
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