AP EAMCET · Maths · Definite Integration
If \(f(x)=\operatorname{Max}\left\{x^3-4, x^4-4\right\}\), and \(g(x)=\operatorname{Min}\left\{x^2, x^3\right\}\), then \(\int_{-1}^1(f(x)-g(x)) d x=\)
- A \(-\frac{151}{20}\)
- B \(\frac{9}{20}\)
- C \(\frac{131}{22}\)
- D \(-\frac{67}{9}\)
Answer & Solution
Correct Answer
(A) \(-\frac{151}{20}\)
Step-by-step Solution
Detailed explanation
For \(x \in [-1, 0]\): \(x^4 \ge x^3\), so \(f(x) = x^4 - 4\). For \(x \in [0, 1]\): \(x^3 \ge x^4\), so \(f(x) = x^3 - 4\). For \(x \in [-1, 1]\): \(x^3 \le x^2\), so \(g(x) = x^3\). For \(x \in [-1, 0]\): \(f(x) - g(x) = (x^4 - 4) - x^3 = x^4 - x^3 - 4\). For \(x \in [0, 1]\):…
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