105. Prove 2* dx < 4 and 3-* dx VI

Q: (a) [ dx ? 元+1

A:

Q: 5- (tanx + secx)2 dx

A:

Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: 4.) Evaluate: xe* dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: S cor* (***) csc (*) da 3x+1) 3 3x+1

A: Solution…

Q: e2 6. - dx -Find 1

A:

Q: -| Vx³ + 16x² dx

A: Let I=∫x3+16x2 dx I=∫xx+16 dx Let assume x+16=t2⇒dx=2t dt I=∫(t2-16)t(2t) dt =2∫(t4-16t2)dt

Q: 6) Evaluate 0.8 1 0 dx 4x² +4

A:

Q: 10) [2* dx

A: given,         ∫2-4xdx

Q: 2 1. xe*dx

A: The value of the integral can be evaluated as following ∫02xexdx

Q: 2 1 dx (3+5x}

A:

Q: Ql Find se dx |

A:

Q: Compute * sin x dx. x4 + 1 p.v.

A:

Q: Find / 5x dx

A: ∫Axndx =A(xn+1n+1)+C, where C is integration constant.

Q: . Evaluate S (-+ 3e* ) dx

A: We have to Evaluate  ∫ {(1/√x) - (2/x) + 3ex} dx = ∫(1/√x) dx - 2 ∫(1/x) dx + 3 ∫ex dx

Q: Lion 1-y If x = Show that 1+y dy V1-y

A:

Q: 4-S e²*sinx dx

A: We have to find the integration of the given function.

Q: dr(sec'x) dx

A:

Q: 5. Comparison Test Determine whether the following integrals converge or diverge. dx

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Q: 1. * dx a <-I 94 dx, a<o

A: (1).  The given integral is: I=∫1∞ xa dx  ;           a&lt;-1

Q: 2) Evaluate: 6+ 1-x² i) dx

A: