1 ∫ 0 X E X 2 D X

प्रश्न

\[\int\limits_0^1 x e^{x^2} dx\]

उत्तर

\[Let\ I = \int_0^1 x\ e^{x^2} d\ x . \]
\[Let\ x^2 = t . Then, 2x\ dx = dt\]
\[When\ x = 0, t = 0\ and\ x\ = 1\, t = 1\]
\[ \therefore I = \frac{1}{2} \int_0^1 e^t\ dt\]
\[ \Rightarrow I = \frac{1}{2} \left( e^t \right)_0^1 \]
\[ \Rightarrow I = \frac{1}{2}\left( e - 1 \right)\]

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Definite Integrals

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 7 Q 6 Q 8

पाठ 19: Definite Integrals - Exercise 20.2 [पृष्ठ ३८]

APPEARS IN

आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12

पाठ 19 Definite Integrals
Exercise 20.2 | Q 7 | पृष्ठ ३८

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