Class 12 • mathematics • Chapter 7
INTEGRALS
True & False Quiz
Antidifferentiate. Accumulate.
✓True
✗False
25
Questions
|
Ch.7
Chapter
|
XII
Class
Why True & False for INTEGRALS?
How this format sharpens your conceptual clarity
🔵 Integration is the inverse process of differentiation and the tool for accumulating quantities like area and volume.
✅ T/F tests substitution vs by-parts choice, partial fractions setup, and properties of definite integrals.
🎯 Trap: indefinite integrals always carry "+C" (family of antiderivatives); dropping it is a scoring error, not just a formality.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
\[ \int x^n\,dx=\frac{x^{n+1}}{n+1}+C,\quad n\ne -1 \]
Q 2
\[ \int \frac{1}{x}\,dx=\ln|x|+C \]
Q 3
\[ \int (f(x)+g(x))\,dx=\int f(x)\,dx+\int g(x)\,dx \]
Q 4
\[ \int 5\,dx=5+C \]
Q 5
\[ \int \cos x\,dx=-\sin x+C \]
Q 6
\[ \int \sec^2 x\,dx=\tan x+C \]
Q 7
\[ \int e^{3x}\,dx=e^{3x}+C \]
Q 8
\[ \int \frac{2x}{x^2+4}\,dx=\ln(x^2+4)+C \]
Q 9
\[ \int \frac{1}{1+x^2}\,dx=\tan^{-1}x+C \]
Q 10
\[ \int \sin^2x\,dx=\frac{x}{2}-\frac{\sin 2x}{4}+C \]
Q 11
\[ \int \frac{1}{\sqrt{1-x^2}}\,dx=\cos^{-1}x+C \]
Q 12
\[ \int \frac{x}{\sqrt{x^2+1}}\,dx=\sqrt{x^2+1}+C \]
Q 13
\[ \int \frac{1}{x^2-1}\,dx=\frac12\ln\left|\frac{x-1}{x+1}\right|+C \]
Q 14
\[ \int x e^x\,dx=xe^x-e^x+C \]
Q 15
\[ \int \ln x\,dx=\frac{1}{x}+C \]
Q 16
\[ \int \frac{dx}{x\ln x}=\ln|\ln x|+C \]
Q 17
\[ \int \frac{dx}{a^2+x^2}=\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)+C,\quad a\ne0 \]
Q 18
\[ \int_0^1 3x^2\,dx=1 \]
Q 19
\[ \int_a^b f(x)\,dx=\int_b^a f(x)\,dx \]
Q 20
\[ \int_a^b f(x)\,dx+\int_b^c f(x)\,dx=\int_a^c f(x)\,dx \]
Q 21
\[ \int_{-a}^{a} f(x)\,dx=0 \]
Q 22
\[ \int_{-a}^{a} x^3\,dx=0,\quad a>0 \]
Q 23
\[ \int_0^{\pi/2}\sin x\,dx=\int_0^{\pi/2}\cos x\,dx \]
Q 24
\[ \int_0^\pi x\sin x\,dx=\pi \]
Q 25
\[ \int_0^1 \frac{x^2}{1+x^2}\,dx=1-\frac{\pi}{4} \]
Key Takeaways — INTEGRALS
Core facts for CBSE Boards & JEE
1
Indefinite integration gives a FAMILY of functions differing by a constant — always add "+C".
2
By the Fundamental Theorem of Calculus, ∫ᵇₐ f(x)dx = F(b)−F(a), where F is any antiderivative of f.
3
ILATE order (Inverse, Log, Algebraic, Trig, Exponential) guides the choice of "u" in integration by parts.
4
∫ᵃ₀ f(x)dx = ∫ᵃ₀ f(a−x)dx — a key property used to simplify definite integrals with symmetry.
5
If f is an odd function, ∫ᵃ−ₐ f(x)dx = 0; if f is even, it equals 2∫ᵃ₀ f(x)dx.
6
Partial fractions apply only to proper rational functions; an improper one needs division first.