જો int limits_0^1 (x^{21}+x^{14}+x^7)(2x^{14} | vedclass

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Question

(C) ધારો કે $I = \int \limits_0^1 (x^{21}+x^{14}+x^7)(2x^{14}+3x^7+6)^{1/7} dx$.$t = 2x^{21} + 3x^{14} + 6x^7$ લેતા,$dt = (42x^{20} + 42x^{13} + 42x^6

Vedclass · Accepted Answer

$63$

Vedclass · Answer

(C) ધારો કે $I = \int \limits_0^1 (x^{21}+x^{14}+x^7)(2x^{14}+3x^7+6)^{1/7} dx$.$t = 2x^{21} + 3x^{14} + 6x^7$ લેતા,$dt = (42x^{20} + 42x^{13} + 42x^6) dx = 42x^6(x^{14} + x^7 + 1) dx$.તેથી,$\int_0^1 (x^{21}+x^{14}+x^7)(2x^{14}+3x^7+6)^{1/7} dx = \frac{1}{42} \int_0^{11} t^{1/7} dt = \frac{1}{42} [\frac{7}{8} t^{8/7}]_0^{11} = \frac{1}{48} (11)^{8/7}$.અહીં $l = 48, m = 8, n = 7$. $m$ અને $n$ પરસ્પર અવિભાજ્ય હોવાથી,$l+m+n = 48+8+7 = 63$.

જો $\int \limits_0^1 (x^{21}+x^{14}+x^7)(2x^{14}+3x^7+6)^{1/7} dx = \frac{1}{l}(11)^{m/n}$ જ્યાં $l, m, n \in N$,$m$ અને $n$ પરસ્પર અવિભાજ્ય હોય,તો $l+m+n$ ની કિંમત $...........$ થાય.

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