This integral can be approached using integration by parts:Let:- u=x ⇒du=dx- dv=11+cosxdx To find v, we need to evaluate ∫11+cosxdx. We can rewrite 1+cosx using the identity:1+cosx=2cos2(x2)Thus,∫11+cosxdx=
= xf(x) - ∫f(x)dx + c [Integration by parts,分部积分]= x(sinx + xcosx) - xsinx + c [Substitution,代入]= x²cosx + c [Simplification,化简] 26004 已知函数f(x)=x2+xsinx+cosx. (1)求f(x)的最小值; (2)若曲线y=f(x)在点(a,f(a))处与直线y=b相切,求a与b的值. (3...
Integration by Parts will be considered
NCERT solutions for CBSE and other state boards is a key requirement for students. Doubtnut helps with homework, doubts and solutions to all the questions. It has helped students get under AIR 100 in NEET & IIT JEE. Get PDF and video solutions of IIT-JEE Mains & Advanced previous year pap...
Integrate (a)∫sinxdx(b)∫sin2xdx(c)∫sinxcosxdx(d)∫sin3xdx Question: Integrate (a)∫sinxdx(b)∫sin2xdx(c)∫sinxcosxdx(d)∫sin3xdx Indefinite integration of Trigonometric functions: Antiderivative of a function f is a function F whose derivative is f :d(F(x))...