Question
Download Solution PDFसमाकलित करा: \(\rm \int \log x \ dx\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
भागानुसार समाकलन:
∫ f(x) g(x) dx = f(x) ∫ g(x) dx - ∫ [f'(x) ∫ g(x) dx] dx.
निश्चित समाकलन:
जर ∫ f(x) dx = g(x) + C असेल, तर \(\rm \int_a^b f(x)\ dx = [ g(x)]_a^b\) = g(b) - g(a).
गणना:
समजा I = ∫ (1)(log x) dx.
log x ला पहिला फलन आणि 1 ला दुसरा फलन मानून, आपल्याला मिळते:
= (log x) ∫ 1 dx - ∫ [\(\rm\frac1x\) ∫ 1 dx] dx
= (log x) x - x + C
= x (log x - 1) + C
Last updated on May 21, 2025
-> Indian Airforce Agniveer Group X 2025 Last date has been extended.
-> Candidates can apply online from 7th to 2nd February 2025.
-> The online examination will be conducted from 22nd March 2025 onwards.
-> The selection of the candidates will depend on three stages which are Phase 1 (Online Written Test), Phase 2 ( DV, Physical Fitness Test, Adaptability Test), and Phase 3 (Medical Examination).
-> The candidates who will qualify all the stages of selection process will be selected for the Air Force Group X posts & will receive a salary ranging of Rs. 30,000.
-> This is one of the most sought jobs. Candidates can also check the Airforce Group X Eligibility here.