int_5^9 frac{log_3 x^2}{log_3 x^2 + log_3(588 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) माना $I = \int_5^9 \frac{\log_3 x^2}{\log_3 x^2 + \log_3(588 - 84x + 3x^2)} dx$. गुणधर्म $\log_3(588 - 84x + 3x^2) = \log_3(3(196 - 28x + x^2)) =

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) माना $I = \int_5^9 \frac{\log_3 x^2}{\log_3 x^2 + \log_3(588 - 84x + 3x^2)} dx$. गुणधर्म $\log_3(588 - 84x + 3x^2) = \log_3(3(196 - 28x + x^2)) = \log_3(3(14 - x)^2)$ का उपयोग करने पर: $I = \int_5^9 \frac{\log_3 x^2}{\log_3 x^2 + \log_3(3(14 - x)^2)} dx \dots (1)$. गुणधर्म $\int_a^b f(x) dx = \int_a^b f(a + b - x) dx$ का उपयोग करने पर,जहाँ $a=5$ और $b=9$,$a+b-x = 14-x$: $I = \int_5^9 \frac{\log_3(14 - x)^2}{\log_3(14 - x)^2 + \log_3(3(14 - (14 - x))^2)} dx$. $I = \int_5^9 \frac{\log_3(14 - x)^2}{\log_3(14 - x)^2 + \log_3(3x^2)} dx \dots (2)$. $(1)$ और $(2)$ को जोड़ने पर: $2I = \int_5^9 \frac{\log_3 x^2 + \log_3(3(14 - x)^2)}{\log_3 x^2 + \log_3(3(14 - x)^2)} dx$. $2I = \int_5^9 1 dx = [x]_5^9 = 9 - 5 = 4$. $I = \frac{4}{2} = 2$.

$\int_5^9 \frac{\log_3 x^2}{\log_3 x^2 + \log_3(588 - 84x + 3x^2)} dx =$

Similar Questions

$\int_0^{\pi /4} {\log (1 + \tan \theta )\,d\theta = } $

यदि $n$ कोई पूर्णांक है,तो $\int_0^\pi {e^{\cos^2 x} \cos^3((2n + 1)x)} \, dx = $

यदि $f(x)$ एक निरंतर आवर्ती फलन है जिसका आवर्तकाल $T$ है,तो समाकलन $I = \int_a^{a + T} {f(x)\,dx} $ है

$\int_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x=$

$\int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec (2023 x)}{1+(2023)^{(2023 x)}} d x=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module