WBJEE · Maths · Definite Integration
Let \(I=\int_{10}^{19} \frac{\sin x}{1+x^{6}} d x\). Then,
- A \(|I| < 10^{-9}\)
- B \(|I| < 10^{-7}\)
- C \(|I| < 10^{-5}\)
- D \(|I|>10^{-7}\)
Answer & Solution
Correct Answer
(B) \(|I| < 10^{-7}\)
Step-by-step Solution
Detailed explanation
For \(x>10,\) we have \(|\sin x| 10^{8}\) \(\Rightarrow \quad \frac{1}{1+x^{8}} \leq 10^{-8}\) \(\therefore \quad\left|\int_{10}^{19} \frac{\sin x}{1+x^{8}} d x\right| \leq \int_{10}^{19} \frac{|\sin x|}{1+x^{8}} d x\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \[
\text { If } f(x)=\begin{array}{|ccc|}
1 & x & x+1\\
2 x & x(x-1) & (x+1)x\\
3 x(x-1) & x(x-1)(x-2) & (x+1)x(x-1)
\end{array}
\] Then, \(f(100)\) is equal toWBJEE 2015 Medium - The value of the integral \(\int \frac{d x}{\left(e^x+e^{-x}\right)^2}\) isWBJEE 2010 Medium
- If \(f(x)=x^{n}, n\) being a non-negative integer, then the values of \(n\) for which
\(f^{\prime}(\alpha+\beta)=f^{\prime}(\alpha)+f^{\prime}(\beta)\) for all \(\alpha, \beta>0\) isWBJEE 2017 Easy - The integrating factor of the differential equation \(x \log x \frac{d y}{d x}+y=2 \log x\) is given byWBJEE 2009 Medium
- The value of the limit \(\lim _{x \rightarrow 1} \frac{\sin \left(e^{x-1}-1\right)}{\log x}\) isWBJEE 2009 Medium
- \(\int_\pi^{16 \pi}|\sin x| d x=\)WBJEE 2011 Easy
More PYQs from WBJEE
- The orange solid on heating gives a colourless gas and a green solid which can be reduced to metal by aluminium powder. The orange and the green solids are, respectivelyWBJEE 2013 Easy
- Let \(f: R \rightarrow R\) be such that \(f(2 x-1)=f(x)\) for all \(x \in R .\) If \(f\) is continuous at \(x=1\) an \(f(1)=1,\) thenWBJEE 2015 Easy
- The limit of the interior angle of a regular polygon of \(n\) sides as \(n \rightarrow \infty\) isWBJEE 2019 Easy
- If for a matrix \(A,|A|=6\) and adj \(A=\left[\begin{array}{ccc}1 & -2, & 4 \\ 4 & 1 & 1 \\ -1 & k & 0\end{array}\right]\), then \(k\) is equal toWBJEE 2025 Medium
- Given that \(\mathrm{f}: \mathrm{S} \rightarrow \mathrm{R}\) is said to have a fixed point at \(\mathrm{c}\) of \(\mathrm{S}\) if \(\mathrm{f}(\mathrm{c})=\mathrm{c}\).
Let \(f:[1, \infty) \rightarrow R\) be defined by \(f(x)=1+\sqrt{x}\). ThenWBJEE 2021 Easy - A unit vector in \(X Y\)-plane making an angle \(45^{\circ}\) with \(\hat{i}+\hat{j}\) and an angle \(60^{\circ}\) with \(3 \hat{i}-4 \hat{j}\) isWBJEE 2024 Easy