Q83.The integral ∫cos(lnx)dx, is equal to (1) x 2 (cos(lnx) −sin(ln x)) + C (2) x(cos(lnx) −sin(ln x)) + C (3) x(cos(lnx) + sin(ln x)) + C (4) x2 (cos(lnx) + sin(ln x)) + C
What This Question Tests
This problem tests the ability to evaluate a definite integral involving a logarithmic function inside a trigonometric function using the technique of integration by parts, potentially multiple times, or recognizing a standard form.
Concepts Tested
Formulas Used
∫u dv = uv - ∫v du
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
13.5 — The Q Value Of A Nuclear Reaction A + B ® C + D Is Defined By
Physics Class 12 · Chapter 13
13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
📋 Question Details
- Chapter
- Indefinite Integration
- Topic
- Integration by parts
- Year
- 2019
- Shift
- 12 Jan Shift 1
- Q Number
- Q83
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 7: Integrals
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