Question:
Evaluate the following integrals:
$\int \frac{1+\sin x}{\sqrt{x-\cos x}} d x$
Solution:
Assume $x-\cos x=t$
$\Rightarrow \mathrm{d}(x-\cos x)=\mathrm{dt}$
$\Rightarrow(1+\sin x) \mathrm{dx}=\mathrm{dt}$
$\therefore$ Substituting $t$ and dt in given equation we get
$\Rightarrow \int \frac{1}{\sqrt{t}} \mathrm{dt}$
$\Rightarrow \int \mathrm{t}^{-1 \backslash 2} \cdot \mathrm{dt}$
$\Rightarrow 2 \mathrm{t}^{1 \backslash 2}+\mathrm{c}$
But $\mathrm{t}=\mathrm{x}-\cos \mathrm{x}$
$\Rightarrow 2(x-\cos x)^{1 / 2}+c$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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