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प्रश्न
Evaluate the following definite integrals: if `int_1^"a" (3x^2 + 2x + 1)*dx` = 11, find a.
उत्तर
Given, `int_1^"a" (3x^2 + 2x + 1)*dx` = 11
∴ `[(3x^3)/3+ (2x^2)/2 + x]_1^"a"` = 11
∴ `[x^3 + x^2 + x]_1^"a"` = 11
∴ (a3 + a2 + a) – (1 + 1 + 1) = 11
∴ a3 + a2 + a – 3 = 11
∴ a3 + a2 + a – 14 = 0
∴ (a – 2)(a2 + 3a + 7) = 0
∴ a = 2 or a2 + 3a + 7 = 0
But a2 + 3a + 7 = 0 does not have eal roots.
∴ a = 2.
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