Help
Contact
For teachers and institutes
Search courses, problems, tests…
A
A
>_
StemPy Lab
Courses ▾
Problems ▾
Practice ▾
Mock Tests
Classes
Community ▾
A
A
The half-angle identity cos²θ = (1 + cos 2θ)/2 is used… | StemPy Lab
Quizzes
/
The half-angle identity cos²θ = (1 + cos 2θ)/2 is used with θ = x/2. Which expression is the antiderivative of cos²x/2?
Mathematics
Medium
High School (11–12)
Functions and Calculus › Integrals
A-Level
AEEE (Amrita)
AMUEEE
AP
AP EAPCET
BCECE
COMEDK UGET
CUET UG
GUJCET
IB
JCECE
JKCET
KCET
KEAM
KIITEE
LPUNEST
MET (Manipal)
MHT-CET
OJEE
SRMJEEE
TS EAPCET
UPESEAT
VITEEE
Created by
StemPy Lab
The half-angle identity
cos
2
θ
=
1
+
cos
2
θ
2
\cos^2\theta = \dfrac{1 + \cos 2\theta}{2}
cos
2
θ
=
2
1
+
cos
2
θ
is used with
θ
=
x
2
\theta = \dfrac{x}{2}
θ
=
2
x
. Which expression is the antiderivative of
cos
2
x
2
\cos^2\dfrac{x}{2}
cos
2
2
x
?
x
2
+
sin
x
\dfrac{x}{2} + \sin x
2
x
+
sin
x
x
2
+
sin
x
4
\dfrac{x}{2} + \dfrac{\sin x}{4}
2
x
+
4
sin
x
x
2
−
sin
x
2
\dfrac{x}{2} - \dfrac{\sin x}{2}
2
x
−
2
sin
x
x
2
+
sin
x
2
\dfrac{x}{2} + \dfrac{\sin x}{2}
2
x
+
2
sin
x
Check Answer
Log in to save
Tag someone
⚑ Report
← All Quizzes
← Which of these is the integral of cot 3x with respect to x on an interval where sin 3x ≠ 0?
To integrate cos³ 2x, a student writes it as cos 2x (1 - sin² 2x) and substitutes u = sin 2x. What antiderivative does she reach? →
More on
Functions and Calculus › Integrals
Discussion (0)
Log in
to join the discussion.
Loading…
Problems on this topic
A student studies the sums Sn = 1/(n + 1) + 1/(n + 2) + … + 1/2n, which have n terms…
Hard
A train on a model railway leaves a station and speeds up, and a meter records its speed…
Hard
Find ∫₀³ (2x + 1) dx as the limit of a right-hand sum…
Medium
Let f(x) = x² - x - 2 = (x - 2)(x + 1). To find ∫₋₂³|f(x)| dx, split the interval where f changes…
Medium
All problems on this topic →