Question Bank - Mathematics

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Evaluate: \(\rm \int \frac{2-5sinx}{cos^2x} dx\)

A.
2tanx - 5secx + C
B.
2tanx + 5secx + C
C.
2cotx - 5secx + C
D.
2tanx - 5cosecx + C

Solution:

Concept:Some useful formulas are:? sec2x dx = tanx + C? tanx secx dx = secx + C\(\rm {1\over cos^2x} = sec^2x\)\(\rm {sinx \over cosx } = tanx\)Calculation:\(\rm ? \frac{2-5sinx}{cos^2x} dx\)= \(\rm ? {2 \over cos^2x} dx - ? {5sinx \over cos^2x} dx\)= ? 2sec2x dx - ? 5 tanx secx dx= 2tanx - 5secx + C ,where C is constant of integration

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