Question
Download Solution PDFमूल्यांकन कीजिए:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
आंशिक भिन्न:
|
हर में भिन्न |
संबंधित आंशिक भिन्न |
|
(x - a) |
|
|
(x – b)2 |
|
|
(x - a) (x – b) |
|
|
(x – c)3 |
|
|
(ax2 + bx + c) |
|
गणना:
यहाँ हमें
माना कि ex = t है और x के संबंध में ex = t का अवकलन करने पर, हमें निम्न प्राप्त होता है
⇒ ex dx = dt या dx = dt/ex = dt/t
माना कि
⇒ 1 = A (t - 1) + B t ---------(1)
(1) के दोनों पक्षों पर t = 0 रखने पर हमें A = - 1 प्राप्त होता है
(1) के दोनों पक्षों पर t = 1 रखने पर हमें B = 1 प्राप्त होता है
चूँकि हम जानते हैं कि
उपरोक्त समीकरण में ex = t रखने पर हमें निम्न प्राप्त होता है
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