Skip to main content
Back to INDEFINITE INTEGRATION

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Medium
1 of 1
Understanding +4 | -1
Assertion : ∫[sin⁡(log⁡x)+cos⁡(log⁡x)]dx=xsin⁡(log⁡x)+C\int[\sin (\log x)+\cos (\log x)] d x=x \sin (\log x)+C

Reason : ddx[xsin⁡(log⁡x)]=sin⁡(log⁡x)+cos⁡(log⁡x)\frac{d}{d x}[x \sin (\log x)]=\sin (\log x)+\cos (\log x).
View answer and explanation
Correct option: A
Assertion is correct, Reason is correct; Reason is a correct explanation for assertion.
Option A is correct because the assertion is true, and the reason correctly explains why the assertion is true. The derivative of xsin⁡(log⁡x)x \sin(\log x) is indeed sin⁡(log⁡x)+cos⁡(log⁡x)\sin(\log x) + \cos(\log x), which validates the integral.

More Questions from INDEFINITE INTEGRATION

Practice All Chapter MCQs →
∫sin⁡5xcos⁡4xdx=\int \sin ^5 x \cos ^4 x d x= If f(x)f(x) is differentibale and ∫0t2xf(x)dx=25t5\int\limits_{0}^{t^2} x f(x) d x=\frac{2}{5} t^5 then f(425)f\left(\frac{4}{25}\right) equals If ∫1−7cos⁡2xsin⁡7xcos⁡2xdx=f(x)sin⁡7x+C\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C is equal to If ∫ex2(2−1x2)de=ex2f(x)+C\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C} and f(12)=2{f}\left(\frac{1}{2}\right)=2, then f(1)f(1) is equal to (where C{C} is an arbitrary constant) ∫x7(1−x2)5dx\int \frac{x^7}{\left(1-x^2\right)^5} d x is equal to: ∫ ax3+  bx2+cx4   dx\int \,\frac{{a{x^3} + \,\,b{x^2} + c}}{{{x^4}}}\;\,dx equals
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →