MHT CET · Maths · Definite Integration
By Simpson rule taking \(n=4\), the value of the integral \(\int_{0}^{1} \frac{1}{1+x^{2}} d x\) is equal to
- A \(0.788\)
- B \(0.781\)
- C \(0.785\)
- D None of these
Answer & Solution
Correct Answer
(C) \(0.785\)
Step-by-step Solution
Detailed explanation
Here, \(h=1 / 4,=0.25, y=\frac{1}{1+x^{2}}\)
By Simpson's Rule
\(
\begin{array}{l}
\int_{0}^{1} \frac{d x}{1+x^{2}}=\frac{1}{4 \times 3} \\
\quad[(1+0.5)+4(0.941+0.64)+2(0.8)] \\
=\frac{1}{12}[9.424]=0.785
\end{array}
\)
| \(x\) | \(y\) | |
| 1 | 0 | 1.0 |
| 2 | 0.25 | 0.941 |
| 3 | 0.5 | 0.8 |
| 4 | 0.75 | 0.64 |
| 5 | 1 | 0.5 |
\(
\begin{array}{l}
\int_{0}^{1} \frac{d x}{1+x^{2}}=\frac{1}{4 \times 3} \\
\quad[(1+0.5)+4(0.941+0.64)+2(0.8)] \\
=\frac{1}{12}[9.424]=0.785
\end{array}
\)
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
- For a sequence if \(S_{n}=\frac{5^{n}-2^{n}}{2^{n}}\), then its fourth term isMHT CET 2020 Medium
- If \(y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots(\mathrm{n} x+1)]^{\frac{3}{2}}\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) at \(x=0\) isMHT CET 2023 Easy
- If \(y=\sec \left(\tan ^{-1} x\right)\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) at \(x=1\) is equal toMHT CET 2024 Easy
- The general solution of the differential equation \(\frac{d y}{d x}=\frac{x+2 y-1}{x+2 y+1}\) isMHT CET 2021 Hard
- The area bounded by the curve \(y=x^{3}\), the \(\mathrm{X}\) -axis and the lines \(x=1\) and \(x=4\) isMHT CET 2020 Easy
- The general solution of the equation \(3 \sec ^2 \theta=2 \operatorname{cosec} \theta\) isMHT CET 2023 Easy
More PYQs from MHT CET
- Capacity of living nucleated cell to differentiate into any other type of cell and form a complete new organism is called _________.MHT CET 2020 Medium
- An electron in stationary hydrogen atom jumps from \(4^{\text {th }}\) energy level to ground level. The velocity that the photon acquired as a result of electron transition will be ( \(h=\) Planck's constant, \(R=\) Rydberg's constant, \(m=\) mass of photon)MHT CET 2022 Hard
- If the points \(P, Q\) and \(R\) are with the position vectors \(\hat{i}-2 \hat{j}+3 \hat{k},-2 \hat{i}+3 \hat{j}+2 \hat{k}\) and \(-8 \hat{i}+13 \hat{j}\) respectively, then these points areMHT CET 2024 Easy
- A pendulum is oscillating with frequency 'n' on the surface of earth. If it is taken to
depth \(\frac{\mathrm{R}}{2}\) below the surface of earth where \(\mathrm{R}\) is radius of earth. New frequency of
oscillations at depth \(\frac{\mathrm{R}}{2}\) isMHT CET 2020 Medium - Figure shows the combination of inductances and capacitances. Resonant frequency of the L - C circuit is
MHT CET 2025 Medium - The solubility of a gas in a liquid is directly proportional to the pressure of the gas over the solution. Identify the law for this statement.MHT CET 2023 Easy