Self Studies
Self Studies
Self Studies
Self Studies

Integrals Test - 42

Result Self Studies

Integrals Test - 42
  • Score

    -

    out of -
  • Rank

    -

    out of -
TIME Taken - -
Self Studies

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Self Studies Self Studies
Weekly Quiz Competition
  • Question 1
    1 / -0
    Evaluate : $$\displaystyle\int^1_0\sqrt{\dfrac{1-x}{1+x}}dx$$
    Solution

  • Question 2
    1 / -0
    Evaluate : $$\displaystyle\int^1_0\dfrac{dx}{(1+x+x^2)}$$
    Solution

  • Question 3
    1 / -0
    Evaluate : $$\displaystyle\int^a_{-a}\sqrt{\dfrac{a-x}{a+x}}dx$$
    Solution

  • Question 4
    1 / -0
    $$\displaystyle\int^a_{-a}x|x|dx=?$$
    Solution
    $$|x|=-x,x<0$$
                  $$x,x>0$$

    $$I=\displaystyle\int^0_{-a}x(-x)dx+\displaystyle\int^a_0x\cdot xdx$$

    $$=\displaystyle\int^0_{-a}-x^2dx+\displaystyle\int^a_0x^2dx$$ 

    $$=\left[\dfrac{-x^3}{3}\right]^0_{-a}+\left[\dfrac{x^3}{3}\right]^a_0=+\dfrac{1}{3}(-a)^3+\dfrac{a^3}{3}=0$$.
  • Question 5
    1 / -0
    $$\displaystyle\int^1_{-2}\dfrac{|x|}{2}dx=?$$
    Solution
    $$|x|=-x,x<0$$
                  $$x,x>0$$

    $$I=\displaystyle\int^0_{-2}\dfrac{-x}{x}dx+\displaystyle\int^1_0\dfrac{x}{x}dx=\displaystyle\int^0_{-2}-dx+\displaystyle\int^1_0dx=[-x]^0_{-2}+[x]^1_0=(-2+1)=-1$$.
  • Question 6
    1 / -0
    Evaluate : $$\displaystyle\int^1_0|2x-1|dx$$
    Solution

  • Question 7
    1 / -0
    Evaluate : $$\displaystyle\int^{\sqrt{2}}_0\sqrt{2-x^2}dx$$
    Solution

  • Question 8
    1 / -0
    Evaluate : $$\displaystyle\int^1_0\dfrac{(1-x)}{(1+x)}dx$$
    Solution

  • Question 9
    1 / -0
    Evaluate : $$\displaystyle\int^2_{-2}|x|dx$$
    Solution

  • Question 10
    1 / -0
    Evaluate : $$\displaystyle\int^1_{-2}|2x+1|dx$$
    Solution

Self Studies
User
Question Analysis

  • Correct -

  • Wrong -

  • Skipped -

My Perfomance
  • Score

    -

    out of -
  • Rank

    -

    out of -
Re-Attempt Weekly Quiz Competition
Selfstudy
Selfstudy
Self Studies Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Self Studies
Click on Allow to receive notifications
Allow Notification
Self Studies
Self Studies Self Studies
To enable notifications follow this 2 steps:
  • First Click on Secure Icon Self Studies
  • Second click on the toggle icon
Allow Notification
Get latest Exam Updates & FREE Study Material Alerts!
Self Studies ×
Open Now