IGDTUW 2025 — Mathematics PYQ
IGDTUW | Mathematics | 2025Evaluate: ∫sinx+3cosx1dx
Choose the correct answer:
- A.
lntan(x+3π)+C
21lntan(2x+6π)+C
Explanation
Solution:
Divide and multiply the denominator by 2:
∫2(21sinx+23cosx)1dx=21∫cos3πsinx+sin3πcosx1dx
21∫sin(x+3π)1dx=21∫csc(x+3π)dx
Using ∫cscθdθ=ln∣tan(θ/2)∣:
21lntan(2x+6π)+C
Correct Option: (b)
Explanation
Solution:
Divide and multiply the denominator by 2:
∫2(21sinx+23cosx)1dx=21∫cos3πsinx+sin3πcosx1dx
21∫sin(x+3π)1dx=21∫csc(x+3π)dx
Using ∫cscθdθ=ln∣tan(θ/2)∣:
21lntan(2x+6π)+C
Correct Option: (b)

