Question
Download Solution PDFअंतिम बिंदु के रूप में x = 0 से x = 4 तक वक्र y = 2e4x के तहत क्षेत्रफल ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
वक्र y = f(x) के क्षेत्रफल को निम्न द्वारा ज्ञात किया गया है:
A =
जहाँ x1 और x2 अंतिम बिंदु हैं जिसके बीच क्षेत्रफल की आवश्यकता होती है।
गणना:
f(x) = y = 2e4x
दिए गए अंतिम बिंदु x1 = 0, x2 = 4 है।
वक्र का क्षेत्रफल (A) = |
⇒ A =
⇒ A =
⇒ A =
⇒ A =
Additional Information
समाकल गुण:
- ∫ xn dx =
+ C ; n ≠ -1 + C - ∫ ex dx = ex+ C
- ∫ ax dx = (ax/ln a) + C ; a > 0, a ≠ 1
- ∫ sin x dx = - cos x + C
- ∫ cos x dx = sin x + C
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