COMEDK · Maths · 30. Definite Integration
The value of \(\int_{-2}^{2}\left(a x^{3}+b x+c\right) d x\) depends on the
- A value of \(b\)
- B value of \(c\)
- C value of \(a\)
- D value of \(a\) and \(b\)
Answer & Solution
Correct Answer
(B) value of \(c\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_{-2}^{2}\left(a x^{3}+b x+c\right) d x\) \[ \begin{aligned} \Rightarrow I=\int_{-2}^{2}\left[\left(a(-2+2-x)^{3}+b(-2+2-x)+c\right)\right] d x \\ & {\left[\because \int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x\right] } \end{aligned} \]…
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
- Given, two vectors \(\hat{\hat{i}}-\hat{\mathfrak{j}}\) and \(\hat{\hat{i}}-2 \hat{\mathfrak{j}}\). The unit vector, coplanar with the two given vectors and perpendicular to \((\hat{\hat{\mathbf{i}}}-\hat{\hat{\mathfrak{j}}})\) isCOMEDK 2015 Easy
- The equation \(\dfrac{x^2}{2-\lambda}+\dfrac{y^2}{\lambda-5}+1=0\) represents an ellipse, ifCOMEDK 2025 Medium
- If \(A=\left[\begin{array}{ccc}1 & -2 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4\end{array}\right]\), then \(A \cdot \operatorname{adj}(A)\) is equal toCOMEDK 2020 Easy
- If \(\vec{a}, \vec{b}, \vec{c}\) are three vectors such that \(a \neq 0\), \(|\vec{a}| = |\vec{c}| = 1, |\vec{b}| = 4\) and \(|\vec{b} \times \vec{c}| = \sqrt{15}\). If \(\vec{b} - 2\vec{c} = \lambda\vec{a}\) then \(\lambda^2\) equals:COMEDK 2025 Medium
- The radius and centre of circle which equation is \(3 x^2+3 y^2+6 x+12 y+5=0\) isCOMEDK 2024 Easy
- \(\int \frac{\operatorname{cosec} x}{\cos ^{2}\left(1+\log \tan \frac{x}{2}\right)} d x=\)COMEDK 2016 Medium
More PYQs from COMEDK
- Which one of the following is an example of step growth polymerisation?COMEDK 2023 Easy
- Arrange the following compounds in the decreasing order of their acidic strength.
(I) m-cresol
(II) Phenol
(III) m-aminophenol
(IV) m-methoxyphenolCOMEDK 2024 Medium - 3 Faraday of electricity is passed through three electrolytic cells connected in series containing \(\mathrm{Ag}^{+}, \mathrm{Ca}^{2+}\) and \(\mathrm{Al}^{+3}\) ions respectively. The molar ratio in which the 3 metal ions are liberated at the electrodes isCOMEDK 2024 Medium
- A hollow prism is filled with water and placed in air. It will deviate the incident raysCOMEDK 2024 Medium
- What is the function platelets?COMEDK 2022 Easy
- 0.4 g of Propane burns completely at 300 K in a bomb calorimeter. The temperature of the calorimeter and surrounding water rises by \(0.4^0 \mathrm{C}\).
If the heat capacity of the calorimeter and contents is \(24 \mathrm{~kJ} \mathrm{~K}^{-1}\) what is the Enthalpy for the reaction?
(Assume that propane gas shows ideal behaviour).COMEDK 2025 Medium