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Integrals

Multiple Choice Questions

1021.
$The integral \int_{1}^{2} e^{x} . x^{2} (2 + \log_{e} (x)) d x = ?$

e(2e - 1)

e(4e + 1)

4e² - 1

e(4e - 1)

e(4e - 1)

$Let y = {(ex)}^{x} \log (y) = [1 = \log (x)] \frac{1}{y} \frac{dy}{dx} = (2 + \log (x)) \Rightarrow dy = {(ex)}^{x} (2 + \log (x)) dx \int_{1}^{2} e^{x} . x^{2} (2 + \log_{e} (x)) d x = {(y)}_{1}^{2} = 4 e^{2} - e$

1022.

The common difference of the A.P. b₁,b₂,....,bm is 2 more than common difference of A.P. a₁,a₂,...,a_n. If a₄₀= –159, a₁₀₀= – 399 and b₁₀₀= a₇₀, then b₁is equal to :

127
81
- 127
- 81

Previous Year Papers

Test Series

Test Yourself

Multiple Choice Questions

1021. The integral ∫12ex . x22 + logexdx = ? e(2e - 1) e(4e + 1) 4e2 - 1 e(4e - 1)

1021.
$The integral \int_{1}^{2} e^{x} . x^{2} (2 + \log_{e} (x)) d x = ?$

e(2e - 1)

e(4e + 1)

4e² - 1

e(4e - 1)