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Mathematics
\[\int e^{cos^2 x} \text{sin 2x dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1 + \cos x}{\left( x + \sin x \right)^3} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
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\[\int\frac{\sin x}{\left( 1 + \cos x \right)^2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\cot x \cdot \log \text{sin x dx}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\sec x \cdot \text{log} \left( \sec x + \tan x \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\text{ ∫ cosec x log} \left( \text{cosec x} - \cot x \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int x^3 \sin \left( x^4 + 1 \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\log x\frac{\text{sin} \left\{ 1 + \left( \log x \right)^2 \right\}}{x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{x^2} \cos^2 \left( \frac{1}{x} \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int \sec^4 \text{ x tan x dx} \]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{x\sqrt{x^4 - 1}} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int4 x^3 \sqrt{5 - x^2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Represent the following graphically:
(i) a displacement of 40 km, 30° east of north
(ii) a displacement of 50 km south-east
(iii) a displacement of 70 km, 40° north of west.
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
Find the magnitude of the vector \[\vec{a} = 2 \hat{i} + 3 \hat{j} - 6 \hat{k} .\]
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
Find the unit vector in the direction of \[3 \hat{i} + 4 \hat{j} - 12 \hat{k} .\]
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is `sqrt(3)`.
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^1 \left( x e^x + \cos\frac{\pi x}{4} \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\limits_0^\pi \frac{\sin x}{\sin x + \cos x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
Evaluate the following integral:
\[\int\limits_{- 1}^1 \left| 2x + 1 \right| dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
