8 ICAR AIEEA PG 2024 - Agricultural Engineering and Technology MCQ (Single Correct) +4 −1 English हिन्दी The value of \(\int_1^3 x^3 \, dx\) will be: निश्चित समाकलन \(\int_1^3 x^3 \, dx\) का मान क्या होगा? A 80 80 Correct Incorrect B 20 20 Correct Incorrect C 27 27 Correct Incorrect D 104 104 Correct Incorrect Check Answer EXPLANATION Differential and Integral Calculus, Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) Evaluating the definite integral using the power rule of integration: \[ \int x^n \, dx = \frac{x^{n+1}}{n+1} \] For \(x^3\): \[ \int_1^3 x^3 \, dx = \left[ \frac{x^4}{4} \right]_1^3 = \frac{3^4}{4} - \frac{1^4}{4} = \frac{81 - 1}{4} = \frac{80}{4} = 20 \] Thus, the value of the integral is 20. निश्चित समाकलन की गणना: \(\int_1^3 x^3 \, dx = \left[\frac{x^4}{4}\right]_1^3 = \frac{3^4 - 1^4}{4} = \frac{81 - 1}{4} = \frac{80}{4} = 20\)। अतः मान 20 होगा। Explanation not matching this question? क्या व्याख्या इस प्रश्न से मेल नहीं खा रही? Report Mismatch त्रुटि बताएं Prev Next
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