Home › TS EAPCET (Engineering) › Mathematics › Integration by Substitution › The integrand is eˣ times the sum of sin x and c…
The integrand is eˣ times the sum of sin x and cos x. Which antiderivative is correct?
Aeˣ(1 − cos x) + C
B2eˣ sin x + C
Ceˣ sin x + C
Deˣ cos x + C
Answer & Solution
Correct answer: C. eˣ sin x + C
With f = sin x the integrand is eˣ(f + f′), and ∫eˣ(f + f′)dx = eˣ f.
Related questions
How can the result of an integration by substitution be checked?Using u = x² + 1, the integral of x(x² + 1)³ between x = 0 and x = 2 evaluates toIn ∫₀² x(x² + 1)³ dx, the substitution u = x² + 1 changes the limits toIf F is an antiderivative of a continuous f, then the integral of f from a to b equalsThe fundamental theorem of calculus shows that differentiation and integration areIn the LIATE rule for choosing u, which type of function comes first in the list?By the LIATE rule, which factor should be chosen as u when integrating x cos x?Integration by substitution is the integral counterpart of which differentiation rule?