The value of integral $\int\limits_{-1}^{1} \frac{\left|x+2\right|}{x+2} dx$ is
- $1$
- $2$
- $0$
- $-1$
The Correct Option is B
Solution and Explanation
Top Questions on Fundamental Theorem of Calculus
- The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
- BITSAT - 2025
- Mathematics
- Fundamental Theorem of Calculus
- Evaluate the sum: $$ \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)} $$
- BITSAT - 2025
- Mathematics
- Fundamental Theorem of Calculus
- Let $ \mathbb{R} $ denote the set of all real numbers. Let $ f: \mathbb{R} \to \mathbb{R} $ be defined by $$ f(x) = \begin{cases} \dfrac{6x + \sin x}{2x + \sin x}, & \text{if } x \ne 0 \\ \dfrac{7}{3}, & \text{if } x = 0 \end{cases} $$ Then which of the following statements is (are) TRUE?
- JEE Advanced - 2025
- Mathematics
- Fundamental Theorem of Calculus
- Let $ x_0 $ be the real number such that $ e^{x_0} + x_0 = 0 $. For a given real number $ \alpha $, define $$ g(x) = \frac{3xe^x + 3x - \alpha e^x - \alpha x}{3(e^x + 1)} $$ for all real numbers $ x $. Then which one of the following statements is TRUE?
- JEE Advanced - 2025
- Mathematics
- Fundamental Theorem of Calculus
- Let $\mathbb{R}$ denote the set of all real numbers. Let $f : \mathbb{R} \to \mathbb{R}$ and $g : \mathbb{R} \to (0,4)$ be functions defined by $$ f(x) = \log_e (x^2 + 2x + 4), \quad \text{and} \quad g(x) = \frac{4}{1 + e^{-2x}}. $$ Define the composite function $f \circ g^{-1}$ by $(f \circ g^{-1})(x) = f(g^{-1}(x))$, where $g^{-1}$ is the inverse of the function $g$. Then the value of the derivative of the composite function $f \circ g^{-1}$ at $x=2$ is _____.
- JEE Advanced - 2025
- Mathematics
- Fundamental Theorem of Calculus
Questions Asked in WBJEE exam
What are the charges stored in the \( 1\,\mu\text{F} \) and \( 2\,\mu\text{F} \) capacitors in the circuit once current becomes steady?
- WBJEE - 2026
- Capacitors and Capacitance
Which one among the following compounds will most readily be dehydrated under acidic condition?
- WBJEE - 2026
- Organic Reactions
Manufacturers supply a zener diode with zener voltage \( V_z=5.6\,\text{V} \) and maximum power dissipation \( P_{\max}=\frac14\,\text{W} \). This zener diode is used in the circuit shown. Calculate the minimum value of the resistance \( R_s \) so that the zener diode will not burn when the input voltage is \( V_{in}=10\,\text{V} \).
- WBJEE - 2026
- Zener Diodes
Two charges \( +q \) and \( -q \) are placed at points \( A \) and \( B \) respectively which are at a distance \( 2L \) apart. \( C \) is the midpoint of \( AB \). The work done in moving a charge \( +Q \) along the semicircle CSD (\( W_1 \)) and along the line CBD (\( W_2 \)) are
- WBJEE - 2026
- electrostatic potential and capacitance
A piece of granite floats at the interface of mercury and water. If the densities of granite, water and mercury are \( \rho, \rho_1, \rho_2 \) respectively, the ratio of volume of granite in water to that in mercury is
- WBJEE - 2026
- Buoyancy and Floatation
Concepts Used:
Fundamental Theorem of Calculus
Fundamental Theorem of Calculus is the theorem which states that differentiation and integration are opposite processes (or operations) of one another.
Calculus's fundamental theorem connects the notions of differentiating and integrating functions. The first portion of the theorem - the first fundamental theorem of calculus – asserts that by integrating f with a variable bound of integration, one of the antiderivatives (also known as an indefinite integral) of a function f, say F, can be derived. This implies the occurrence of antiderivatives for continuous functions.