Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
1.6k views
in Integrals calculus by (41.3k points)

Let f(x) = [b2 + (a - 1)b  + 2]x - ∫(sin2x + cos4x)dx be an increasing function of x ∈ R and b ∈ R. Then a can take value(s) 

(A) 0 

(B) 1 

(C) 2 

(D) 4

1 Answer

+1 vote
by (41.5k points)
selected by
 
Best answer

Answer is  (A), (B), (C)

f′(x) = b2 + (a – 1)b + 2 – sin2x – cos4x

f′(x) = b2 + (a – 1)b + 2 – 1

For increasing function, f′(x) > 0, so

D < 0

⇒ (a − 1)2 − 4 < 0

⇒ a ∈ (−1, 3)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...