Question
Download Solution PDFयदि f(x) = 2x है, तो \(\int^{10}_2\frac{f'(x)}{f(x)}dx\) किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
f(x) = 2x
प्रयुक्त सूत्र:
\(\rm \frac{d}{dx} a^{x} = (In\: a).a^{x}\)
\(\rm \int 1.dx = x + C\)
\(\rm \int_{a}^{b} f(x) dx = F(b) - F(a)\), जहां \(\rm \int f(x).dx = F(x) + C\)
गणना:
हमारे पास f(x) = 2x ---- (i) है
⇒ f'(x) = 2x In(2) ----(ii)
अब, हमें \(\rm \int^{10}_2\frac{f'(x)}{f(x)}dx\) का मान ज्ञात करना है
फॉर्म समीकरण (i) और (ii), हम प्राप्त करते हैं
⇒ \(\rm \int^{10}_2 \frac{2^{x} In(2)}{2^{x}} dx\)
⇒ \(\rm \int^{10}_2 { In(2)} \space dx\)
⇒ \(\)In(2) [10 - 2]
⇒ 8 In(2)
∴\(\rm \int^{10}_2\frac{f'(x)}{f(x)}dx\) का मान 8 In(2) के बराबर है।
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